Simplify 11/(b-7)-(2b-3)/(b-7)

$\frac{11}{b - 7} - \frac{2 b - 3}{b - 7}$

Step 1

Combine the numerators over the common denominator.

$\frac{11 - (2 b - 3)}{b - 7}$

Step 2

Simplify each term.

Apply the distributive property.

$\frac{11 - (2 b) - - 3}{b - 7}$

Multiply $2$ by $- 1$ .

$\frac{11 - 2 b - - 3}{b - 7}$

Multiply $- 1$ by $- 3$ .

$\frac{11 - 2 b + 3}{b - 7}$

Step 3

Simplify terms.

Add $11$ and $3$ .

$\frac{- 2 b + 14}{b - 7}$

Factor $2$ out of $- 2 b + 14$ .

Factor $2$ out of $- 2 b$ .

$\frac{2 (- b) + 14}{b - 7}$

Factor $2$ out of $14$ .

$\frac{2 (- b) + 2 (7)}{b - 7}$

Factor $2$ out of $2 (- b) + 2 (7)$ .

$\frac{2 (- b + 7)}{b - 7}$

Cancel the common factor of $- b + 7$ and $b - 7$ .

Factor $- 1$ out of $- b$ .

$\frac{2 (- (b) + 7)}{b - 7}$

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{2 (- (b) - 1 (- 7))}{b - 7}$

Factor $- 1$ out of $- (b) - 1 (- 7)$ .

$\frac{2 (- (b - 7))}{b - 7}$

Rewrite $- (b - 7)$ as $- 1 (b - 7)$ .

$\frac{2 (- 1 (b - 7))}{b - 7}$

Cancel the common factor.

$\frac{2 (- 1 (b - 7))}{b - 7}$

Divide $2 \cdot (- 1)$ by $1$ .

$2 \cdot (- 1)$

Multiply $2$ by $- 1$ .

$- 2$