Simplify (-5x-1)/(x+2)+(2x-5)/(x+2)

$\frac{- 5 x - 1}{x + 2} + \frac{2 x - 5}{x + 2}$

Step 1

Combine the numerators over the common denominator.

$\frac{- 5 x - 1 + 2 x - 5}{x + 2}$

Step 2

Add $- 5 x$ and $2 x$ .

$\frac{- 3 x - 1 - 5}{x + 2}$

Step 3

Subtract $5$ from $- 1$ .

$\frac{- 3 x - 6}{x + 2}$

Step 4

Factor $3$ out of $- 3 x - 6$ .

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) - 6}{x + 2}$

Factor $3$ out of $- 6$ .

$\frac{3 (- x) + 3 (- 2)}{x + 2}$

Factor $3$ out of $3 (- x) + 3 (- 2)$ .

$\frac{3 (- x - 2)}{x + 2}$

Step 5

Cancel the common factor of $- x - 2$ and $x + 2$ .

Factor $- 1$ out of $- x$ .

$\frac{3 (- (x) - 2)}{x + 2}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{3 (- (x) - 1 (2))}{x + 2}$

Factor $- 1$ out of $- (x) - 1 (2)$ .

$\frac{3 (- (x + 2))}{x + 2}$

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

$\frac{3 (- 1 (x + 2))}{x + 2}$

Cancel the common factor.

$\frac{3 (- 1 (x + 2))}{x + 2}$

Divide $3 \cdot (- 1)$ by $1$ .

$3 \cdot (- 1)$

Step 6

Multiply $3$ by $- 1$ .

$- 3$