Solve x+1-6x+12/x-2/x-5+frac{11x-22{x-2}}

$$\frac { \frac { x + 1 - 6 x + 12 } { x - 2 } } { x - 5 + \frac { 11 x - 22 } { x - 2 } }$$

Evaluate

$$\frac{13-5x}{\left(x-2\right)\left(x+6\right)}$$

Short Solution Steps

Combine x and -6x to get -5x.

$$\frac{\frac{-5x+1+12}{x-2}}{x-5+\frac{11x-22}{x-2}}$$

Add 1 and 12 to get 13.

$$\frac{\frac{-5x+13}{x-2}}{x-5+\frac{11x-22}{x-2}}$$

Factor the expressions that are not already factored in \frac{11x-22}{x-2}.

$$\frac{\frac{-5x+13}{x-2}}{x-5+\frac{11\left(x-2\right)}{x-2}}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{\frac{-5x+13}{x-2}}{x-5+11}$$

Add -5 and 11 to get 6.

$$\frac{\frac{-5x+13}{x-2}}{x+6}$$

Express \frac{\frac{-5x+13}{x-2}}{x+6} as a single fraction.

$$\frac{-5x+13}{\left(x-2\right)\left(x+6\right)}$$

Apply the distributive property by multiplying each term of x-2 by each term of x+6.

$$\frac{-5x+13}{x^{2}+6x-2x-12}$$

Combine 6x and -2x to get 4x.

$$\frac{-5x+13}{x^{2}+4x-12}$$

Expand

$$\frac{13-5x}{\left(x-2\right)\left(x+6\right)}$$

Short Solution Steps

Combine x and -6x to get -5x.

$$\frac{\frac{-5x+1+12}{x-2}}{x-5+\frac{11x-22}{x-2}}$$

Add 1 and 12 to get 13.

$$\frac{\frac{-5x+13}{x-2}}{x-5+\frac{11x-22}{x-2}}$$

Factor the expressions that are not already factored in \frac{11x-22}{x-2}.

$$\frac{\frac{-5x+13}{x-2}}{x-5+\frac{11\left(x-2\right)}{x-2}}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{\frac{-5x+13}{x-2}}{x-5+11}$$

Add -5 and 11 to get 6.

$$\frac{\frac{-5x+13}{x-2}}{x+6}$$

Express \frac{\frac{-5x+13}{x-2}}{x+6} as a single fraction.

$$\frac{-5x+13}{\left(x-2\right)\left(x+6\right)}$$

Apply the distributive property by multiplying each term of x-2 by each term of x+6.

$$\frac{-5x+13}{x^{2}+6x-2x-12}$$

Combine 6x and -2x to get 4x.

$$\frac{-5x+13}{x^{2}+4x-12}$$