Simplify (x+12)/(2x-5)-(3x-2)/(2x-5)

$\frac{x + 12}{2 x - 5} - \frac{3 x - 2}{2 x - 5}$

Combine the numerators over the common denominator.

$\frac{x + 12 - (3 x - 2)}{2 x - 5}$

Simplify each term.

Apply the distributive property.

$\frac{x + 12 - (3 x) - - 2}{2 x - 5}$

Multiply $3$ by $- 1$ .

$\frac{x + 12 - 3 x - - 2}{2 x - 5}$

Multiply $- 1$ by $- 2$ .

$\frac{x + 12 - 3 x + 2}{2 x - 5}$

Simplify terms.

Subtract $3 x$ from $x$ .

$\frac{- 2 x + 12 + 2}{2 x - 5}$

Add $12$ and $2$ .

$\frac{- 2 x + 14}{2 x - 5}$

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

Factor $2$ out of $- 2 x$ .

$\frac{2 (- x) + 14}{2 x - 5}$

Factor $2$ out of $14$ .

$\frac{2 (- x) + 2 (7)}{2 x - 5}$

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

$\frac{2 (- x + 7)}{2 x - 5}$

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

$\frac{2 (- (x) + 7)}{2 x - 5}$

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

$\frac{2 (- (x) - 1 (- 7))}{2 x - 5}$

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

$\frac{2 (- (x - 7))}{2 x - 5}$

Simplify the expression.

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

$\frac{2 (- 1 (x - 7))}{2 x - 5}$

Move the negative in front of the fraction.

$- \frac{2 (x - 7)}{2 x - 5}$