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

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

Multiply the numerator and denominator of the complex fraction by $(x + 4) (x - 3)$ .

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $x + 4$ .

Move the leading negative in $- \frac{1}{x + 4}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 3$ .

Move the leading negative in $- \frac{3}{x - 3}$ into the numerator.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 3$ .

Move the leading negative in $- \frac{4}{x - 3}$ into the numerator.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Apply the distributive property.

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

Move $- 1$ to the left of $x$ .

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

Multiply $- 3$ by $- 1$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Apply the distributive property.

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

Move $- 3$ to the left of $x$ .

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

Multiply $4$ by $- 3$ .

$\frac{- x + 3 - 3 \cdot x - 12}{x - 3 + (x + 4) \cdot - 4}$

Subtract $3 x$ from $- x$ .

$\frac{- 4 x + 3 - 12}{x - 3 + (x + 4) \cdot - 4}$

Subtract $12$ from $3$ .

$\frac{- 4 x - 9}{x - 3 + (x + 4) \cdot - 4}$

Simplify the denominator.

Apply the distributive property.

$\frac{- 4 x - 9}{x - 3 + x \cdot - 4 + 4 \cdot - 4}$

Move $- 4$ to the left of $x$ .

$\frac{- 4 x - 9}{x - 3 - 4 \cdot x + 4 \cdot - 4}$

Multiply $4$ by $- 4$ .

$\frac{- 4 x - 9}{x - 3 - 4 \cdot x - 16}$

Subtract $4 x$ from $x$ .

$\frac{- 4 x - 9}{- 3 x - 3 - 16}$

Subtract $16$ from $- 3$ .

$\frac{- 4 x - 9}{- 3 x - 19}$

Simplify terms.

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) - 9}{- 3 x - 19}$

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

$\frac{- (4 x) - 1 (9)}{- 3 x - 19}$

Factor $- 1$ out of $- (4 x) - 1 (9)$ .

$\frac{- (4 x + 9)}{- 3 x - 19}$

Rewrite $- (4 x + 9)$ as $- 1 (4 x + 9)$ .

$\frac{- 1 (4 x + 9)}{- 3 x - 19}$

Factor $- 1$ out of $- 3 x$ .

$\frac{- 1 (4 x + 9)}{- (3 x) - 19}$

Rewrite $- 19$ as $- 1 (19)$ .

$\frac{- 1 (4 x + 9)}{- (3 x) - 1 (19)}$

Factor $- 1$ out of $- (3 x) - 1 (19)$ .

$\frac{- 1 (4 x + 9)}{- (3 x + 19)}$

Rewrite $- (3 x + 19)$ as $- 1 (3 x + 19)$ .

$\frac{- 1 (4 x + 9)}{- 1 (3 x + 19)}$

Cancel the common factor.

$\frac{- 1 (4 x + 9)}{- 1 (3 x + 19)}$

Rewrite the expression.

$\frac{4 x + 9}{3 x + 19}$

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

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