Solve 18x^2+8/x-6+9x^2-12/6-x

$$\frac { 18 x ^ { 2 } + 8 } { x - 6 } + \frac { 9 x ^ { 2 } - 12 } { 6 - x }$$

Evaluate

$$\frac{9x^{2}+20}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and 6-x is x-6. Multiply \frac{9x^{2}-12}{6-x} times \frac{-1}{-1}.

$$\frac{18x^{2}+8}{x-6}+\frac{-\left(9x^{2}-12\right)}{x-6}$$

Since \frac{18x^{2}+8}{x-6} and \frac{-\left(9x^{2}-12\right)}{x-6} have the same denominator, add them by adding their numerators.

$$\frac{18x^{2}+8-\left(9x^{2}-12\right)}{x-6}$$

Do the multiplications in 18x^{2}+8-\left(9x^{2}-12\right).

$$\frac{18x^{2}+8-9x^{2}+12}{x-6}$$

Combine like terms in 18x^{2}+8-9x^{2}+12.

$$\frac{9x^{2}+20}{x-6}$$

Expand

$$\frac{9x^{2}+20}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and 6-x is x-6. Multiply \frac{9x^{2}-12}{6-x} times \frac{-1}{-1}.

$$\frac{18x^{2}+8}{x-6}+\frac{-\left(9x^{2}-12\right)}{x-6}$$

Since \frac{18x^{2}+8}{x-6} and \frac{-\left(9x^{2}-12\right)}{x-6} have the same denominator, add them by adding their numerators.

$$\frac{18x^{2}+8-\left(9x^{2}-12\right)}{x-6}$$

Do the multiplications in 18x^{2}+8-\left(9x^{2}-12\right).

$$\frac{18x^{2}+8-9x^{2}+12}{x-6}$$

Combine like terms in 18x^{2}+8-9x^{2}+12.

$$\frac{9x^{2}+20}{x-6}$$