Simplify (7x+2)/(x-6)+5/(6-x)

$\frac{7 x + 2}{x - 6} + \frac{5}{6 - x}$

Step 1

Simplify terms.

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

$\frac{7 x + 2}{x - 6} + \frac{5}{- 1 (- 6) - x}$

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

$\frac{7 x + 2}{x - 6} + \frac{5}{- 1 (- 6) - (x)}$

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

$\frac{7 x + 2}{x - 6} + \frac{5}{- 1 (- 6 + x)}$

Simplify the expression.

Move a negative from the denominator of $\frac{5}{- 1 (- 6 + x)}$ to the numerator.

$\frac{7 x + 2}{x - 6} + \frac{- 1 \cdot 5}{- 6 + x}$

Reorder terms.

$\frac{7 x + 2}{x - 6} + \frac{- 1 \cdot 5}{x - 6}$

Combine the numerators over the common denominator.

$\frac{7 x + 2 - 1 \cdot 5}{x - 6}$

Step 2

Simplify the numerator.

Multiply $- 1$ by $5$ .

$\frac{7 x + 2 - 5}{x - 6}$

Subtract $5$ from $2$ .

$\frac{7 x - 3}{x - 6}$