Solve 3/4*1/6x-3/4*1/3-3x-1frac{1}{2}

$$\frac { 3 } { 4 } \times \frac { 1 } { 6 x } - \frac { 3 } { 4 } \times \frac { 1 } { 3 } - 3 x - 1 \frac { 1 } { 2 }$$

Evaluate

$$-3x-\frac{7}{4}+\frac{1}{8x}$$

Short Solution Steps

Multiply \frac{3}{4} times \frac{1}{6x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4\times 6x}-\frac{3}{4}\times \frac{1}{3}-3x-\frac{1\times 2+1}{2}$$

Multiply \frac{3}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4\times 6x}-\frac{3\times 1}{4\times 3}-3x-\frac{1\times 2+1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3}{4\times 6x}-\frac{1}{4}-3x-\frac{1\times 2+1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\times 6x and 4 is 4\times 6x. Multiply \frac{1}{4} times \frac{6x}{6x}.

$$\frac{3}{4\times 6x}-\frac{6x}{4\times 6x}-3x-\frac{1\times 2+1}{2}$$

Since \frac{3}{4\times 6x} and \frac{6x}{4\times 6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-6x}{4\times 6x}-3x-\frac{1\times 2+1}{2}$$

Factor the expressions that are not already factored in \frac{3-6x}{4\times 6x}.

$$\frac{3\left(-2x+1\right)}{4\times 6x}-3x-\frac{1\times 2+1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 4x and 2 is 2\times 4x. Multiply \frac{3}{2} times \frac{4x}{4x}.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{3\times 4x}{2\times 4x}$$

Since \frac{-2x+1}{2\times 4x} and \frac{3\times 4x}{2\times 4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2x+1-3\times 4x}{2\times 4x}-3x$$

Do the multiplications in -2x+1-3\times 4x.

$$\frac{-2x+1-12x}{2\times 4x}-3x$$

Combine like terms in -2x+1-12x.

$$\frac{-14x+1}{2\times 4x}-3x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x times \frac{2\times 4x}{2\times 4x}.

$$\frac{-14x+1}{2\times 4x}+\frac{-3x\times 2\times 4x}{2\times 4x}$$

Since \frac{-14x+1}{2\times 4x} and \frac{-3x\times 2\times 4x}{2\times 4x} have the same denominator, add them by adding their numerators.

$$\frac{-14x+1-3x\times 2\times 4x}{2\times 4x}$$

Do the multiplications in -14x+1-3x\times 2\times 4x.

$$\frac{-14x+1-24x^{2}}{2\times 4x}$$

Factor the expressions that are not already factored in \frac{-14x+1-24x^{2}}{2\times 4x}.

$$\frac{-24\left(x-\left(-\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{2\times 4x}$$

Cancel out 2\times 4 in both numerator and denominator.

$$\frac{-3\left(x-\left(-\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

To find the opposite of -\frac{1}{24}\sqrt{73}-\frac{7}{24}, find the opposite of each term.

$$\frac{-3\left(x-\left(-\frac{1}{24}\sqrt{73}\right)-\left(-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

The opposite of -\frac{1}{24}\sqrt{73} is \frac{1}{24}\sqrt{73}.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}-\left(-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

The opposite of -\frac{7}{24} is \frac{7}{24}.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

To find the opposite of \frac{1}{24}\sqrt{73}-\frac{7}{24}, find the opposite of each term.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}-\left(-\frac{7}{24}\right)\right)}{x}$$

The opposite of -\frac{7}{24} is \frac{7}{24}.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Use the distributive property to multiply -3 by x+\frac{1}{24}\sqrt{73}+\frac{7}{24}.

$$\frac{\left(-3x-3\times \frac{1}{24}\sqrt{73}-3\times \frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Multiply -3 and \frac{1}{24} to get \frac{-3}{24}.

$$\frac{\left(-3x+\frac{-3}{24}\sqrt{73}-3\times \frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Reduce the fraction \frac{-3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}-3\times \frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Express -3\times \frac{7}{24} as a single fraction.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}+\frac{-3\times 7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Multiply -3 and 7 to get -21.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}+\frac{-21}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}-\frac{7}{8}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Apply the distributive property by multiplying each term of -3x-\frac{1}{8}\sqrt{73}-\frac{7}{8} by each term of x-\frac{1}{24}\sqrt{73}+\frac{7}{24}.

$$\frac{-3x^{2}-3x\left(-\frac{1}{24}\right)\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\sqrt{73}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply \sqrt{73} and \sqrt{73} to get 73.

$$\frac{-3x^{2}-3x\left(-\frac{1}{24}\right)\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Express -3\left(-\frac{1}{24}\right) as a single fraction.

$$\frac{-3x^{2}+\frac{-3\left(-1\right)}{24}x\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -3 and -1 to get 3.

$$\frac{-3x^{2}+\frac{3}{24}x\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Express -3\times \frac{7}{24} as a single fraction.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}+\frac{-3\times 7}{24}x-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -3 and 7 to get -21.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}+\frac{-21}{24}x-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}-\frac{7}{8}x-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Combine \frac{1}{8}x\sqrt{73} and -\frac{1}{8}\sqrt{73}x to get 0.

$$\frac{-3x^{2}-\frac{7}{8}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Express -\frac{1}{8}\times 73 as a single fraction.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{-73}{8}\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Fraction \frac{-73}{8} can be rewritten as -\frac{73}{8} by extracting the negative sign.

$$\frac{-3x^{2}-\frac{7}{8}x-\frac{73}{8}\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{73}{8} times -\frac{1}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{-73\left(-1\right)}{8\times 24}-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Do the multiplications in the fraction \frac{-73\left(-1\right)}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{1}{8} times \frac{7}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}+\frac{-7}{8\times 24}\sqrt{73}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Do the multiplications in the fraction \frac{-7}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}+\frac{-7}{192}\sqrt{73}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Fraction \frac{-7}{192} can be rewritten as -\frac{7}{192} by extracting the negative sign.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Combine -\frac{7}{8}x and -\frac{7}{8}x to get -\frac{7}{4}x.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{7}{8} times -\frac{1}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}+\frac{-7\left(-1\right)}{8\times 24}\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Do the multiplications in the fraction \frac{-7\left(-1\right)}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}+\frac{7}{192}\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Combine -\frac{7}{192}\sqrt{73} and \frac{7}{192}\sqrt{73} to get 0.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{7}{8} times \frac{7}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}+\frac{-7\times 7}{8\times 24}}{x}$$

Do the multiplications in the fraction \frac{-7\times 7}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}+\frac{-49}{192}}{x}$$

Fraction \frac{-49}{192} can be rewritten as -\frac{49}{192} by extracting the negative sign.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{49}{192}}{x}$$

Since \frac{73}{192} and \frac{49}{192} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73-49}{192}}{x}$$

Subtract 49 from 73 to get 24.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{24}{192}}{x}$$

Reduce the fraction \frac{24}{192} to lowest terms by extracting and canceling out 24.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{1}{8}}{x}$$

Expand

$$-3x-\frac{7}{4}+\frac{1}{8x}$$

Short Solution Steps

Multiply \frac{3}{4} times \frac{1}{6x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4\times 6x}-\frac{3}{4}\times \frac{1}{3}-3x-\frac{1\times 2+1}{2}$$

Multiply \frac{3}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4\times 6x}-\frac{3\times 1}{4\times 3}-3x-\frac{1\times 2+1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3}{4\times 6x}-\frac{1}{4}-3x-\frac{1\times 2+1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\times 6x and 4 is 4\times 6x. Multiply \frac{1}{4} times \frac{6x}{6x}.

$$\frac{3}{4\times 6x}-\frac{6x}{4\times 6x}-3x-\frac{1\times 2+1}{2}$$

Since \frac{3}{4\times 6x} and \frac{6x}{4\times 6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-6x}{4\times 6x}-3x-\frac{1\times 2+1}{2}$$

Factor the expressions that are not already factored in \frac{3-6x}{4\times 6x}.

$$\frac{3\left(-2x+1\right)}{4\times 6x}-3x-\frac{1\times 2+1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 4x and 2 is 2\times 4x. Multiply \frac{3}{2} times \frac{4x}{4x}.

$$\frac{-2x+1}{2\times 4x}-3x-\frac{3\times 4x}{2\times 4x}$$

Since \frac{-2x+1}{2\times 4x} and \frac{3\times 4x}{2\times 4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2x+1-3\times 4x}{2\times 4x}-3x$$

Do the multiplications in -2x+1-3\times 4x.

$$\frac{-2x+1-12x}{2\times 4x}-3x$$

Combine like terms in -2x+1-12x.

$$\frac{-14x+1}{2\times 4x}-3x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x times \frac{2\times 4x}{2\times 4x}.

$$\frac{-14x+1}{2\times 4x}+\frac{-3x\times 2\times 4x}{2\times 4x}$$

Since \frac{-14x+1}{2\times 4x} and \frac{-3x\times 2\times 4x}{2\times 4x} have the same denominator, add them by adding their numerators.

$$\frac{-14x+1-3x\times 2\times 4x}{2\times 4x}$$

Do the multiplications in -14x+1-3x\times 2\times 4x.

$$\frac{-14x+1-24x^{2}}{2\times 4x}$$

Factor the expressions that are not already factored in \frac{-14x+1-24x^{2}}{2\times 4x}.

$$\frac{-24\left(x-\left(-\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{2\times 4x}$$

Cancel out 2\times 4 in both numerator and denominator.

$$\frac{-3\left(x-\left(-\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

To find the opposite of -\frac{1}{24}\sqrt{73}-\frac{7}{24}, find the opposite of each term.

$$\frac{-3\left(x-\left(-\frac{1}{24}\sqrt{73}\right)-\left(-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

The opposite of -\frac{1}{24}\sqrt{73} is \frac{1}{24}\sqrt{73}.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}-\left(-\frac{7}{24}\right)\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

The opposite of -\frac{7}{24} is \frac{7}{24}.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)\left(x-\left(\frac{1}{24}\sqrt{73}-\frac{7}{24}\right)\right)}{x}$$

To find the opposite of \frac{1}{24}\sqrt{73}-\frac{7}{24}, find the opposite of each term.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}-\left(-\frac{7}{24}\right)\right)}{x}$$

The opposite of -\frac{7}{24} is \frac{7}{24}.

$$\frac{-3\left(x+\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Use the distributive property to multiply -3 by x+\frac{1}{24}\sqrt{73}+\frac{7}{24}.

$$\frac{\left(-3x-3\times \frac{1}{24}\sqrt{73}-3\times \frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Multiply -3 and \frac{1}{24} to get \frac{-3}{24}.

$$\frac{\left(-3x+\frac{-3}{24}\sqrt{73}-3\times \frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Reduce the fraction \frac{-3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}-3\times \frac{7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Express -3\times \frac{7}{24} as a single fraction.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}+\frac{-3\times 7}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Multiply -3 and 7 to get -21.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}+\frac{-21}{24}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\left(-3x-\frac{1}{8}\sqrt{73}-\frac{7}{8}\right)\left(x-\frac{1}{24}\sqrt{73}+\frac{7}{24}\right)}{x}$$

Apply the distributive property by multiplying each term of -3x-\frac{1}{8}\sqrt{73}-\frac{7}{8} by each term of x-\frac{1}{24}\sqrt{73}+\frac{7}{24}.

$$\frac{-3x^{2}-3x\left(-\frac{1}{24}\right)\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\sqrt{73}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply \sqrt{73} and \sqrt{73} to get 73.

$$\frac{-3x^{2}-3x\left(-\frac{1}{24}\right)\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Express -3\left(-\frac{1}{24}\right) as a single fraction.

$$\frac{-3x^{2}+\frac{-3\left(-1\right)}{24}x\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -3 and -1 to get 3.

$$\frac{-3x^{2}+\frac{3}{24}x\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}-3x\times \frac{7}{24}-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Express -3\times \frac{7}{24} as a single fraction.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}+\frac{-3\times 7}{24}x-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -3 and 7 to get -21.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}+\frac{-21}{24}x-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-3x^{2}+\frac{1}{8}x\sqrt{73}-\frac{7}{8}x-\frac{1}{8}\sqrt{73}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Combine \frac{1}{8}x\sqrt{73} and -\frac{1}{8}\sqrt{73}x to get 0.

$$\frac{-3x^{2}-\frac{7}{8}x-\frac{1}{8}\times 73\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Express -\frac{1}{8}\times 73 as a single fraction.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{-73}{8}\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Fraction \frac{-73}{8} can be rewritten as -\frac{73}{8} by extracting the negative sign.

$$\frac{-3x^{2}-\frac{7}{8}x-\frac{73}{8}\left(-\frac{1}{24}\right)-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{73}{8} times -\frac{1}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{-73\left(-1\right)}{8\times 24}-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Do the multiplications in the fraction \frac{-73\left(-1\right)}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}-\frac{1}{8}\sqrt{73}\times \frac{7}{24}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{1}{8} times \frac{7}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}+\frac{-7}{8\times 24}\sqrt{73}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Do the multiplications in the fraction \frac{-7}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}+\frac{-7}{192}\sqrt{73}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Fraction \frac{-7}{192} can be rewritten as -\frac{7}{192} by extracting the negative sign.

$$\frac{-3x^{2}-\frac{7}{8}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}-\frac{7}{8}x-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Combine -\frac{7}{8}x and -\frac{7}{8}x to get -\frac{7}{4}x.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}-\frac{7}{8}\left(-\frac{1}{24}\right)\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{7}{8} times -\frac{1}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}+\frac{-7\left(-1\right)}{8\times 24}\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Do the multiplications in the fraction \frac{-7\left(-1\right)}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{192}\sqrt{73}+\frac{7}{192}\sqrt{73}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Combine -\frac{7}{192}\sqrt{73} and \frac{7}{192}\sqrt{73} to get 0.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{7}{8}\times \frac{7}{24}}{x}$$

Multiply -\frac{7}{8} times \frac{7}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}+\frac{-7\times 7}{8\times 24}}{x}$$

Do the multiplications in the fraction \frac{-7\times 7}{8\times 24}.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}+\frac{-49}{192}}{x}$$

Fraction \frac{-49}{192} can be rewritten as -\frac{49}{192} by extracting the negative sign.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73}{192}-\frac{49}{192}}{x}$$

Since \frac{73}{192} and \frac{49}{192} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{73-49}{192}}{x}$$

Subtract 49 from 73 to get 24.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{24}{192}}{x}$$

Reduce the fraction \frac{24}{192} to lowest terms by extracting and canceling out 24.

$$\frac{-3x^{2}-\frac{7}{4}x+\frac{1}{8}}{x}$$