Simplify (2x+7)/(x-6)+2/(6-x)

$\frac{2 x + 7}{x - 6} + \frac{2}{6 - x}$

Simplify terms.

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{2 x + 7}{x - 6} + \frac{2}{- 1 (- 6) - x}$

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

$\frac{2 x + 7}{x - 6} + \frac{2}{- 1 (- 6) - (x)}$

Factor $- 1$ out of $- 1 (- 6) - (x)$ .

$\frac{2 x + 7}{x - 6} + \frac{2}{- 1 (- 6 + x)}$

Simplify the expression.

Move a negative from the denominator of $\frac{2}{- 1 (- 6 + x)}$ to the numerator.

$\frac{2 x + 7}{x - 6} + \frac{- 1 \cdot 2}{- 6 + x}$

Reorder terms.

$\frac{2 x + 7}{x - 6} + \frac{- 1 \cdot 2}{x - 6}$

Combine the numerators over the common denominator.

$\frac{2 x + 7 - 1 \cdot 2}{x - 6}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{2 x + 7 - 2}{x - 6}$

Subtract $2$ from $7$ .

$\frac{2 x + 5}{x - 6}$