Simplify (x-1)/(15x+12)+(8-2x)/(15x+12)

$\frac{x - 1}{15 x + 12} + \frac{8 - 2 x}{15 x + 12}$

Step 1

Combine the numerators over the common denominator.

$\frac{x - 1 + 8 - 2 x}{15 x + 12}$

Step 2

Subtract $2 x$ from $x$ .

$\frac{- x - 1 + 8}{15 x + 12}$

Step 3

Add $- 1$ and $8$ .

$\frac{- x + 7}{15 x + 12}$

Step 4

Factor $3$ out of $15 x + 12$ .

Factor $3$ out of $15 x$ .

$\frac{- x + 7}{3 (5 x) + 12}$

Factor $3$ out of $12$ .

$\frac{- x + 7}{3 (5 x) + 3 (4)}$

Factor $3$ out of $3 (5 x) + 3 (4)$ .

$\frac{- x + 7}{3 (5 x + 4)}$

Step 5

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

$\frac{- (x) + 7}{3 (5 x + 4)}$

Step 6

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

$\frac{- (x) - 1 (- 7)}{3 (5 x + 4)}$

Step 7

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

$\frac{- (x - 7)}{3 (5 x + 4)}$

Step 8

Simplify the expression.

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

$\frac{- 1 (x - 7)}{3 (5 x + 4)}$

Move the negative in front of the fraction.

$- \frac{x - 7}{3 (5 x + 4)}$