Simplify (-4/(x+7)+2/(x-7))/(-3/(x-7))

$\frac{- \frac{4}{x + 7} + \frac{2}{x - 7}}{- \frac{3}{x - 7}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(- \frac{4}{x + 7} + \frac{2}{x - 7}) (- \frac{x - 7}{3})$

Step 2

To write $- \frac{4}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x - 7}{x - 7}$ .

$(- \frac{4}{x + 7} \cdot \frac{x - 7}{x - 7} + \frac{2}{x - 7}) (- \frac{x - 7}{3})$

Step 3

To write $\frac{2}{x - 7}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$(- \frac{4}{x + 7} \cdot \frac{x - 7}{x - 7} + \frac{2}{x - 7} \cdot \frac{x + 7}{x + 7}) (- \frac{x - 7}{3})$

Step 4

Write each expression with a common denominator of $(x + 7) (x - 7)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x + 7}$ by $\frac{x - 7}{x - 7}$ .

$(- \frac{4 (x - 7)}{(x + 7) (x - 7)} + \frac{2}{x - 7} \cdot \frac{x + 7}{x + 7}) (- \frac{x - 7}{3})$

Multiply $\frac{2}{x - 7}$ by $\frac{x + 7}{x + 7}$ .

$(- \frac{4 (x - 7)}{(x + 7) (x - 7)} + \frac{2 (x + 7)}{(x - 7) (x + 7)}) (- \frac{x - 7}{3})$

Reorder the factors of $(x - 7) (x + 7)$ .

$(- \frac{4 (x - 7)}{(x + 7) (x - 7)} + \frac{2 (x + 7)}{(x + 7) (x - 7)}) (- \frac{x - 7}{3})$

Step 5

Simplify terms.

Combine the numerators over the common denominator.

$\frac{- 4 (x - 7) + 2 (x + 7)}{(x + 7) (x - 7)} (- \frac{x - 7}{3})$

Rewrite using the commutative property of multiplication.

$- \frac{- 4 (x - 7) + 2 (x + 7)}{(x + 7) (x - 7)} \cdot \frac{x - 7}{3}$

Cancel the common factor of $x - 7$ .

Move the leading negative in $- \frac{- 4 (x - 7) + 2 (x + 7)}{(x + 7) (x - 7)}$ into the numerator.

$\frac{- (- 4 (x - 7) + 2 (x + 7))}{(x + 7) (x - 7)} \cdot \frac{x - 7}{3}$

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

$\frac{- (- 4 (x - 7) + 2 (x + 7))}{(x - 7) (x + 7)} \cdot \frac{x - 7}{3}$

Cancel the common factor.

$\frac{- (- 4 (x - 7) + 2 (x + 7))}{(x - 7) (x + 7)} \cdot \frac{x - 7}{3}$

Rewrite the expression.

$\frac{- (- 4 (x - 7) + 2 (x + 7))}{x + 7} \cdot \frac{1}{3}$

Multiply $\frac{- (- 4 (x - 7) + 2 (x + 7))}{x + 7}$ by $\frac{1}{3}$ .

$\frac{- (- 4 (x - 7) + 2 (x + 7))}{(x + 7) \cdot 3}$

Step 6

Simplify the numerator.

Factor $2$ out of $- 4 (x - 7) + 2 (x + 7)$ .

Factor $2$ out of $- 4 (x - 7)$ .

$\frac{- (2 (- 2 (x - 7)) + 2 (x + 7))}{(x + 7) \cdot 3}$

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

$\frac{- (2 (- 2 (x - 7) + x + 7))}{(x + 7) \cdot 3}$

Apply the distributive property.

$\frac{- (2 (- 2 x - 2 \cdot - 7 + x + 7))}{(x + 7) \cdot 3}$

Multiply $- 2$ by $- 7$ .

$\frac{- (2 (- 2 x + 14 + x + 7))}{(x + 7) \cdot 3}$

Add $- 2 x$ and $x$ .

$\frac{- (2 (- x + 14 + 7))}{(x + 7) \cdot 3}$

Add $14$ and $7$ .

$\frac{- 1 \cdot 2 (- x + 21)}{(x + 7) \cdot 3}$

Multiply $- 1$ by $2$ .

$\frac{- 2 (- x + 21)}{(x + 7) \cdot 3}$

Step 7

Simplify with factoring out.

Move $3$ to the left of $x + 7$ .

$\frac{- 2 (- x + 21)}{3 \cdot (x + 7)}$

Move the negative in front of the fraction.

$- \frac{(2) (- x + 21)}{3 \cdot (x + 7)}$

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

$- \frac{2 (- (x) + 21)}{3 (x + 7)}$

Rewrite $21$ as $- 1 (- 21)$ .

$- \frac{2 (- (x) - 1 (- 21))}{3 (x + 7)}$

Factor $- 1$ out of $- (x) - 1 (- 21)$ .

$- \frac{2 (- (x - 21))}{3 (x + 7)}$

Simplify the expression.

Rewrite $- (x - 21)$ as $- 1 (x - 21)$ .

$- \frac{2 (- 1 (x - 21))}{3 (x + 7)}$

Move the negative in front of the fraction.

$- - \frac{2 (x - 21)}{3 (x + 7)}$

Multiply $- 1$ by $- 1$ .

$1 \frac{2 (x - 21)}{3 (x + 7)}$

Multiply $\frac{2 (x - 21)}{3 (x + 7)}$ by $1$ .

$\frac{2 (x - 21)}{3 (x + 7)}$

Simplify (-4/(x+7)+2/(x-7))/(-3/(x-7))

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