Simplify 5/(7-x)+3/(x-7)

$\frac{5}{7 - x} + \frac{3}{x - 7}$

Factor $- 1$ out of $x$ .

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

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

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

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

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

Simplify the expression.

Move a negative from the denominator of $\frac{3}{- 1 (- x + 7)}$ to the numerator.

$\frac{5}{7 - x} + \frac{- 1 \cdot 3}{- x + 7}$

Reorder terms.

$\frac{5}{- x + 7} + \frac{- 1 \cdot 3}{- x + 7}$

Combine the numerators over the common denominator.

$\frac{5 - 1 \cdot 3}{- x + 7}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$\frac{5 - 3}{- x + 7}$

Subtract $3$ from $5$ .

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

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

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

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

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

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

$\frac{2}{- (x - 7)}$

Rewrite negatives.

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

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

Move the negative in front of the fraction.

$- \frac{2}{x - 7}$