Solve 2x-3/4-3+x/675x-1/6-3+x/24-frac{1}{6}

$$\frac{ 2x-3 }{ 4 } - \frac{ 3+x }{ 6 } 7 \frac{ 5x-1 }{ 6 } - \frac{ 3+x }{ 24 } - \frac{ 1 }{ 6 }$$

Evaluate

$$-\frac{35x^{2}}{36}-\frac{163x}{72}-\frac{11}{24}$$

Short Solution Steps

Express \frac{3+x}{6}\times 7 as a single fraction.

$$\frac{2x-3}{4}-\frac{\left(3+x\right)\times 7}{6}\times \frac{5x-1}{6}-\frac{3+x}{24}-\frac{1}{6}$$

Multiply \frac{\left(3+x\right)\times 7}{6} times \frac{5x-1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x-3}{4}-\frac{\left(3+x\right)\times 7\left(5x-1\right)}{6\times 6}-\frac{3+x}{24}-\frac{1}{6}$$

Multiply 6 and 6 to get 36.

$$\frac{2x-3}{4}-\frac{\left(3+x\right)\times 7\left(5x-1\right)}{36}-\frac{3+x}{24}-\frac{1}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 36 is 36. Multiply \frac{2x-3}{4} times \frac{9}{9}.

$$\frac{9\left(2x-3\right)}{36}-\frac{\left(3+x\right)\times 7\left(5x-1\right)}{36}-\frac{3+x}{24}-\frac{1}{6}$$

Since \frac{9\left(2x-3\right)}{36} and \frac{\left(3+x\right)\times 7\left(5x-1\right)}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\left(2x-3\right)-\left(3+x\right)\times 7\left(5x-1\right)}{36}-\frac{3+x}{24}-\frac{1}{6}$$

Do the multiplications in 9\left(2x-3\right)-\left(3+x\right)\times 7\left(5x-1\right).

$$\frac{18x-27-105x+21-35x^{2}+7x}{36}-\frac{3+x}{24}-\frac{1}{6}$$

Combine like terms in 18x-27-105x+21-35x^{2}+7x.

$$\frac{-80x-6-35x^{2}}{36}-\frac{3+x}{24}-\frac{1}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 24 is 72. Multiply \frac{-80x-6-35x^{2}}{36} times \frac{2}{2}. Multiply \frac{3+x}{24} times \frac{3}{3}.

$$\frac{2\left(-80x-6-35x^{2}\right)}{72}-\frac{3\left(3+x\right)}{72}-\frac{1}{6}$$

Since \frac{2\left(-80x-6-35x^{2}\right)}{72} and \frac{3\left(3+x\right)}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-80x-6-35x^{2}\right)-3\left(3+x\right)}{72}-\frac{1}{6}$$

Do the multiplications in 2\left(-80x-6-35x^{2}\right)-3\left(3+x\right).

$$\frac{-160x-12-70x^{2}-9-3x}{72}-\frac{1}{6}$$

Combine like terms in -160x-12-70x^{2}-9-3x.

$$\frac{-163x-21-70x^{2}}{72}-\frac{1}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 72 and 6 is 72. Multiply \frac{1}{6} times \frac{12}{12}.

$$\frac{-163x-21-70x^{2}}{72}-\frac{12}{72}$$

Since \frac{-163x-21-70x^{2}}{72} and \frac{12}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-163x-21-70x^{2}-12}{72}$$

Combine like terms in -163x-21-70x^{2}-12.

$$\frac{-163x-33-70x^{2}}{72}$$

Expand

$$-\frac{35x^{2}}{36}-\frac{163x}{72}-\frac{11}{24}$$

Short Solution Steps

Express \frac{3+x}{6}\times 7 as a single fraction.

$$\frac{2x-3}{4}-\frac{\left(3+x\right)\times 7}{6}\times \frac{5x-1}{6}-\frac{3+x}{24}-\frac{1}{6}$$

Multiply \frac{\left(3+x\right)\times 7}{6} times \frac{5x-1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x-3}{4}-\frac{\left(3+x\right)\times 7\left(5x-1\right)}{6\times 6}-\frac{3+x}{24}-\frac{1}{6}$$

Multiply 6 and 6 to get 36.

$$\frac{2x-3}{4}-\frac{\left(3+x\right)\times 7\left(5x-1\right)}{36}-\frac{3+x}{24}-\frac{1}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 36 is 36. Multiply \frac{2x-3}{4} times \frac{9}{9}.

$$\frac{9\left(2x-3\right)}{36}-\frac{\left(3+x\right)\times 7\left(5x-1\right)}{36}-\frac{3+x}{24}-\frac{1}{6}$$

Since \frac{9\left(2x-3\right)}{36} and \frac{\left(3+x\right)\times 7\left(5x-1\right)}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\left(2x-3\right)-\left(3+x\right)\times 7\left(5x-1\right)}{36}-\frac{3+x}{24}-\frac{1}{6}$$

Do the multiplications in 9\left(2x-3\right)-\left(3+x\right)\times 7\left(5x-1\right).

$$\frac{18x-27-105x+21-35x^{2}+7x}{36}-\frac{3+x}{24}-\frac{1}{6}$$

Combine like terms in 18x-27-105x+21-35x^{2}+7x.

$$\frac{-80x-6-35x^{2}}{36}-\frac{3+x}{24}-\frac{1}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 24 is 72. Multiply \frac{-80x-6-35x^{2}}{36} times \frac{2}{2}. Multiply \frac{3+x}{24} times \frac{3}{3}.

$$\frac{2\left(-80x-6-35x^{2}\right)}{72}-\frac{3\left(3+x\right)}{72}-\frac{1}{6}$$

Since \frac{2\left(-80x-6-35x^{2}\right)}{72} and \frac{3\left(3+x\right)}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-80x-6-35x^{2}\right)-3\left(3+x\right)}{72}-\frac{1}{6}$$

Do the multiplications in 2\left(-80x-6-35x^{2}\right)-3\left(3+x\right).

$$\frac{-160x-12-70x^{2}-9-3x}{72}-\frac{1}{6}$$

Combine like terms in -160x-12-70x^{2}-9-3x.

$$\frac{-163x-21-70x^{2}}{72}-\frac{1}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 72 and 6 is 72. Multiply \frac{1}{6} times \frac{12}{12}.

$$\frac{-163x-21-70x^{2}}{72}-\frac{12}{72}$$

Since \frac{-163x-21-70x^{2}}{72} and \frac{12}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-163x-21-70x^{2}-12}{72}$$

Combine like terms in -163x-21-70x^{2}-12.

$$\frac{-163x-33-70x^{2}}{72}$$