Simplify (4/(x+5)-6/(x+3))/(-1/(x+5))

$\frac{\frac{4}{x + 5} - \frac{6}{x + 3}}{- \frac{1}{x + 5}}$

Multiply the numerator by the reciprocal of the denominator.

$(\frac{4}{x + 5} - \frac{6}{x + 3}) (- (x + 5))$

To write $\frac{4}{x + 5}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$(\frac{4}{x + 5} \cdot \frac{x + 3}{x + 3} - \frac{6}{x + 3}) (- (x + 5))$

To write $- \frac{6}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x + 5}{x + 5}$ .

$(\frac{4}{x + 5} \cdot \frac{x + 3}{x + 3} - \frac{6}{x + 3} \cdot \frac{x + 5}{x + 5}) (- (x + 5))$

Write each expression with a common denominator of $(x + 5) (x + 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{x + 5}$ by $\frac{x + 3}{x + 3}$ .

$(\frac{4 (x + 3)}{(x + 5) (x + 3)} - \frac{6}{x + 3} \cdot \frac{x + 5}{x + 5}) (- (x + 5))$

Multiply $\frac{6}{x + 3}$ by $\frac{x + 5}{x + 5}$ .

$(\frac{4 (x + 3)}{(x + 5) (x + 3)} - \frac{6 (x + 5)}{(x + 3) (x + 5)}) (- (x + 5))$

Reorder the factors of $(x + 5) (x + 3)$ .

$(\frac{4 (x + 3)}{(x + 3) (x + 5)} - \frac{6 (x + 5)}{(x + 3) (x + 5)}) (- (x + 5))$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{4 (x + 3) - 6 (x + 5)}{(x + 3) (x + 5)} (- (x + 5))$

Rewrite using the commutative property of multiplication.

$- \frac{4 (x + 3) - 6 (x + 5)}{(x + 3) (x + 5)} (x + 5)$

Cancel the common factor of $x + 5$ .

Move the leading negative in $- \frac{4 (x + 3) - 6 (x + 5)}{(x + 3) (x + 5)}$ into the numerator.

$\frac{- (4 (x + 3) - 6 (x + 5))}{(x + 3) (x + 5)} (x + 5)$

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

$\frac{- (4 (x + 3) - 6 (x + 5))}{(x + 5) (x + 3)} (x + 5)$

Cancel the common factor.

$\frac{- (4 (x + 3) - 6 (x + 5))}{(x + 5) (x + 3)} (x + 5)$

Rewrite the expression.

$\frac{- (4 (x + 3) - 6 (x + 5))}{x + 3}$

Simplify the numerator.

Factor $2$ out of $4 (x + 3) - 6 (x + 5)$ .

Factor $2$ out of $4 (x + 3)$ .

$\frac{- (2 (2 (x + 3)) - 6 (x + 5))}{x + 3}$

Factor $2$ out of $- 6 (x + 5)$ .

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

Factor $2$ out of $2 (2 (x + 3)) + 2 (- 3 (x + 5))$ .

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

Apply the distributive property.

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

Multiply $2$ by $3$ .

$\frac{- (2 (2 x + 6 - 3 (x + 5)))}{x + 3}$

Apply the distributive property.

$\frac{- (2 (2 x + 6 - 3 x - 3 \cdot 5))}{x + 3}$

Multiply $- 3$ by $5$ .

$\frac{- (2 (2 x + 6 - 3 x - 15))}{x + 3}$

Subtract $3 x$ from $2 x$ .

$\frac{- (2 (- x + 6 - 15))}{x + 3}$

Subtract $15$ from $6$ .

$\frac{- 1 \cdot 2 (- x - 9)}{x + 3}$

Multiply $- 1$ by $2$ .

$\frac{- 2 (- x - 9)}{x + 3}$

Simplify with factoring out.

Move the negative in front of the fraction.

$- \frac{(2) (- x - 9)}{x + 3}$

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

$- \frac{2 (- (x) - 9)}{x + 3}$

Rewrite $- 9$ as $- 1 (9)$ .

$- \frac{2 (- (x) - 1 (9))}{x + 3}$

Factor $- 1$ out of $- (x) - 1 (9)$ .

$- \frac{2 (- (x + 9))}{x + 3}$

Simplify the expression.

Rewrite $- (x + 9)$ as $- 1 (x + 9)$ .

$- \frac{2 (- 1 (x + 9))}{x + 3}$

Move the negative in front of the fraction.

$- - \frac{2 (x + 9)}{x + 3}$

Multiply $- 1$ by $- 1$ .

$1 \frac{2 (x + 9)}{x + 3}$

Multiply $\frac{2 (x + 9)}{x + 3}$ by $1$ .

$\frac{2 (x + 9)}{x + 3}$

Simplify (4/(x+5)-6/(x+3))/(-1/(x+5))

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