Pre-Algebra Examples

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

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 $15 x + 12$ .

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Step 4.1

Factor $3$ out of $15 x$ .

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

Step 4.2

Factor $3$ out of $12$ .

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

Step 4.3

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.

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Step 8.1

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

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

Step 8.2

Move the negative in front of the fraction.

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