Solve 3x+9+4x+5/3x-6

$$3x+9+ \frac{ 4x+5 }{ 3x-6 }$$

Evaluate

$$\frac{9x^{2}+13x-49}{3\left(x-2\right)}$$

Short Solution Steps

Factor 3x-6.

$$3x+9+\frac{4x+5}{3\left(x-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x+9 times \frac{3\left(x-2\right)}{3\left(x-2\right)}.

$$\frac{\left(3x+9\right)\times 3\left(x-2\right)}{3\left(x-2\right)}+\frac{4x+5}{3\left(x-2\right)}$$

Since \frac{\left(3x+9\right)\times 3\left(x-2\right)}{3\left(x-2\right)} and \frac{4x+5}{3\left(x-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x+9\right)\times 3\left(x-2\right)+4x+5}{3\left(x-2\right)}$$

Do the multiplications in \left(3x+9\right)\times 3\left(x-2\right)+4x+5.

$$\frac{9x^{2}-18x+27x-54+4x+5}{3\left(x-2\right)}$$

Combine like terms in 9x^{2}-18x+27x-54+4x+5.

$$\frac{9x^{2}+13x-49}{3\left(x-2\right)}$$

Factor the expressions that are not already factored in \frac{9x^{2}+13x-49}{3\left(x-2\right)}.

$$\frac{9\left(x-\left(-\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{3\left(x-2\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\left(x-\left(-\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

To find the opposite of -\frac{1}{18}\sqrt{1933}-\frac{13}{18}, find the opposite of each term.

$$\frac{3\left(x-\left(-\frac{1}{18}\sqrt{1933}\right)-\left(-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

The opposite of -\frac{1}{18}\sqrt{1933} is \frac{1}{18}\sqrt{1933}.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}-\left(-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

The opposite of -\frac{13}{18} is \frac{13}{18}.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

To find the opposite of \frac{1}{18}\sqrt{1933}-\frac{13}{18}, find the opposite of each term.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}-\left(-\frac{13}{18}\right)\right)}{x-2}$$

The opposite of -\frac{13}{18} is \frac{13}{18}.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Use the distributive property to multiply 3 by x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}.

$$\frac{\left(3x+3\times \frac{1}{18}\sqrt{1933}+3\times \frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Multiply 3 and \frac{1}{18} to get \frac{3}{18}.

$$\frac{\left(3x+\frac{3}{18}\sqrt{1933}+3\times \frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+3\times \frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Express 3\times \frac{13}{18} as a single fraction.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+\frac{3\times 13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Multiply 3 and 13 to get 39.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+\frac{39}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Reduce the fraction \frac{39}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+\frac{13}{6}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Apply the distributive property by multiplying each term of 3x+\frac{1}{6}\sqrt{1933}+\frac{13}{6} by each term of x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}.

$$\frac{3x^{2}+3x\left(-\frac{1}{18}\right)\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\sqrt{1933}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \sqrt{1933} and \sqrt{1933} to get 1933.

$$\frac{3x^{2}+3x\left(-\frac{1}{18}\right)\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Express 3\left(-\frac{1}{18}\right) as a single fraction.

$$\frac{3x^{2}+\frac{3\left(-1\right)}{18}x\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply 3 and -1 to get -3.

$$\frac{3x^{2}+\frac{-3}{18}x\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Reduce the fraction \frac{-3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Express 3\times \frac{13}{18} as a single fraction.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+\frac{3\times 13}{18}x+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply 3 and 13 to get 39.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+\frac{39}{18}x+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Reduce the fraction \frac{39}{18} to lowest terms by extracting and canceling out 3.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+\frac{13}{6}x+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Combine -\frac{1}{6}x\sqrt{1933} and \frac{1}{6}\sqrt{1933}x to get 0.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{1}{6} and 1933 to get \frac{1933}{6}.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{1933}{6}\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{1933}{6} times -\frac{1}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{1933\left(-1\right)}{6\times 18}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Do the multiplications in the fraction \frac{1933\left(-1\right)}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{-1933}{108}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Fraction \frac{-1933}{108} can be rewritten as -\frac{1933}{108} by extracting the negative sign.

$$\frac{3x^{2}+\frac{13}{6}x-\frac{1933}{108}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{1}{6} times \frac{13}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{6}x-\frac{1933}{108}+\frac{1\times 13}{6\times 18}\sqrt{1933}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Do the multiplications in the fraction \frac{1\times 13}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{6}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Combine \frac{13}{6}x and \frac{13}{6}x to get \frac{13}{3}x.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{13}{6} times -\frac{1}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{13\left(-1\right)}{6\times 18}\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Do the multiplications in the fraction \frac{13\left(-1\right)}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{-13}{108}\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Fraction \frac{-13}{108} can be rewritten as -\frac{13}{108} by extracting the negative sign.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}-\frac{13}{108}\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Combine \frac{13}{108}\sqrt{1933} and -\frac{13}{108}\sqrt{1933} to get 0.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{13}{6} times \frac{13}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13\times 13}{6\times 18}}{x-2}$$

Do the multiplications in the fraction \frac{13\times 13}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{169}{108}}{x-2}$$

Since -\frac{1933}{108} and \frac{169}{108} have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+\frac{13}{3}x+\frac{-1933+169}{108}}{x-2}$$

Add -1933 and 169 to get -1764.

$$\frac{3x^{2}+\frac{13}{3}x+\frac{-1764}{108}}{x-2}$$

Reduce the fraction \frac{-1764}{108} to lowest terms by extracting and canceling out 36.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{49}{3}}{x-2}$$

Expand

$$\frac{9x^{2}+13x-49}{3\left(x-2\right)}$$

Short Solution Steps

Factor 3x-6.

$$3x+9+\frac{4x+5}{3\left(x-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x+9 times \frac{3\left(x-2\right)}{3\left(x-2\right)}.

$$\frac{\left(3x+9\right)\times 3\left(x-2\right)}{3\left(x-2\right)}+\frac{4x+5}{3\left(x-2\right)}$$

Since \frac{\left(3x+9\right)\times 3\left(x-2\right)}{3\left(x-2\right)} and \frac{4x+5}{3\left(x-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x+9\right)\times 3\left(x-2\right)+4x+5}{3\left(x-2\right)}$$

Do the multiplications in \left(3x+9\right)\times 3\left(x-2\right)+4x+5.

$$\frac{9x^{2}-18x+27x-54+4x+5}{3\left(x-2\right)}$$

Combine like terms in 9x^{2}-18x+27x-54+4x+5.

$$\frac{9x^{2}+13x-49}{3\left(x-2\right)}$$

Factor the expressions that are not already factored in \frac{9x^{2}+13x-49}{3\left(x-2\right)}.

$$\frac{9\left(x-\left(-\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{3\left(x-2\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\left(x-\left(-\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

To find the opposite of -\frac{1}{18}\sqrt{1933}-\frac{13}{18}, find the opposite of each term.

$$\frac{3\left(x-\left(-\frac{1}{18}\sqrt{1933}\right)-\left(-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

The opposite of -\frac{1}{18}\sqrt{1933} is \frac{1}{18}\sqrt{1933}.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}-\left(-\frac{13}{18}\right)\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

The opposite of -\frac{13}{18} is \frac{13}{18}.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)\left(x-\left(\frac{1}{18}\sqrt{1933}-\frac{13}{18}\right)\right)}{x-2}$$

To find the opposite of \frac{1}{18}\sqrt{1933}-\frac{13}{18}, find the opposite of each term.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}-\left(-\frac{13}{18}\right)\right)}{x-2}$$

The opposite of -\frac{13}{18} is \frac{13}{18}.

$$\frac{3\left(x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Use the distributive property to multiply 3 by x+\frac{1}{18}\sqrt{1933}+\frac{13}{18}.

$$\frac{\left(3x+3\times \frac{1}{18}\sqrt{1933}+3\times \frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Multiply 3 and \frac{1}{18} to get \frac{3}{18}.

$$\frac{\left(3x+\frac{3}{18}\sqrt{1933}+3\times \frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+3\times \frac{13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Express 3\times \frac{13}{18} as a single fraction.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+\frac{3\times 13}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Multiply 3 and 13 to get 39.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+\frac{39}{18}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Reduce the fraction \frac{39}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\left(3x+\frac{1}{6}\sqrt{1933}+\frac{13}{6}\right)\left(x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}\right)}{x-2}$$

Apply the distributive property by multiplying each term of 3x+\frac{1}{6}\sqrt{1933}+\frac{13}{6} by each term of x-\frac{1}{18}\sqrt{1933}+\frac{13}{18}.

$$\frac{3x^{2}+3x\left(-\frac{1}{18}\right)\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\sqrt{1933}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \sqrt{1933} and \sqrt{1933} to get 1933.

$$\frac{3x^{2}+3x\left(-\frac{1}{18}\right)\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Express 3\left(-\frac{1}{18}\right) as a single fraction.

$$\frac{3x^{2}+\frac{3\left(-1\right)}{18}x\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply 3 and -1 to get -3.

$$\frac{3x^{2}+\frac{-3}{18}x\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Reduce the fraction \frac{-3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+3x\times \frac{13}{18}+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Express 3\times \frac{13}{18} as a single fraction.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+\frac{3\times 13}{18}x+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply 3 and 13 to get 39.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+\frac{39}{18}x+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Reduce the fraction \frac{39}{18} to lowest terms by extracting and canceling out 3.

$$\frac{3x^{2}-\frac{1}{6}x\sqrt{1933}+\frac{13}{6}x+\frac{1}{6}\sqrt{1933}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Combine -\frac{1}{6}x\sqrt{1933} and \frac{1}{6}\sqrt{1933}x to get 0.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{1}{6}\times 1933\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{1}{6} and 1933 to get \frac{1933}{6}.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{1933}{6}\left(-\frac{1}{18}\right)+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{1933}{6} times -\frac{1}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{1933\left(-1\right)}{6\times 18}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Do the multiplications in the fraction \frac{1933\left(-1\right)}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{6}x+\frac{-1933}{108}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Fraction \frac{-1933}{108} can be rewritten as -\frac{1933}{108} by extracting the negative sign.

$$\frac{3x^{2}+\frac{13}{6}x-\frac{1933}{108}+\frac{1}{6}\sqrt{1933}\times \frac{13}{18}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{1}{6} times \frac{13}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{6}x-\frac{1933}{108}+\frac{1\times 13}{6\times 18}\sqrt{1933}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Do the multiplications in the fraction \frac{1\times 13}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{6}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{13}{6}x+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Combine \frac{13}{6}x and \frac{13}{6}x to get \frac{13}{3}x.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{13}{6}\left(-\frac{1}{18}\right)\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{13}{6} times -\frac{1}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{13\left(-1\right)}{6\times 18}\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Do the multiplications in the fraction \frac{13\left(-1\right)}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}+\frac{-13}{108}\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Fraction \frac{-13}{108} can be rewritten as -\frac{13}{108} by extracting the negative sign.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{108}\sqrt{1933}-\frac{13}{108}\sqrt{1933}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Combine \frac{13}{108}\sqrt{1933} and -\frac{13}{108}\sqrt{1933} to get 0.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13}{6}\times \frac{13}{18}}{x-2}$$

Multiply \frac{13}{6} times \frac{13}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{13\times 13}{6\times 18}}{x-2}$$

Do the multiplications in the fraction \frac{13\times 13}{6\times 18}.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{1933}{108}+\frac{169}{108}}{x-2}$$

Since -\frac{1933}{108} and \frac{169}{108} have the same denominator, add them by adding their numerators.

$$\frac{3x^{2}+\frac{13}{3}x+\frac{-1933+169}{108}}{x-2}$$

Add -1933 and 169 to get -1764.

$$\frac{3x^{2}+\frac{13}{3}x+\frac{-1764}{108}}{x-2}$$

Reduce the fraction \frac{-1764}{108} to lowest terms by extracting and canceling out 36.

$$\frac{3x^{2}+\frac{13}{3}x-\frac{49}{3}}{x-2}$$