Evaluate 8/(a-4)+(2a)/(4-a)

$\frac{8}{a - 4} + \frac{2 a}{4 - a}$

Simplify terms.

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{8}{a - 4} + \frac{2 a}{- 1 (- 4) - a}$

Factor $- 1$ out of $- a$ .

$\frac{8}{a - 4} + \frac{2 a}{- 1 (- 4) - (a)}$

Factor $- 1$ out of $- 1 (- 4) - (a)$ .

$\frac{8}{a - 4} + \frac{2 a}{- 1 (- 4 + a)}$

Simplify the expression.

Move a negative from the denominator of $\frac{2 a}{- 1 (- 4 + a)}$ to the numerator.

$\frac{8}{a - 4} + \frac{- (2 a)}{- 4 + a}$

Reorder terms.

$\frac{8}{a - 4} + \frac{- (2 a)}{a - 4}$

Combine the numerators over the common denominator.

$\frac{8 - (2 a)}{a - 4}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{8 - 2 a}{a - 4}$

Factor $2$ out of $8 - 2 a$ .

Factor $2$ out of $8$ .

$\frac{2 (4) - 2 a}{a - 4}$

Factor $2$ out of $- 2 a$ .

$\frac{2 (4) + 2 (- a)}{a - 4}$

Factor $2$ out of $2 (4) + 2 (- a)$ .

$\frac{2 (4 - a)}{a - 4}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4 - a$ and $a - 4$ .

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{2 (- 1 (- 4) - a)}{a - 4}$

Factor $- 1$ out of $- a$ .

$\frac{2 (- 1 (- 4) - (a))}{a - 4}$

Factor $- 1$ out of $- 1 (- 4) - (a)$ .

$\frac{2 (- 1 (- 4 + a))}{a - 4}$

Reorder terms.

$\frac{2 (- 1 (a - 4))}{a - 4}$

Cancel the common factor.

$\frac{2 (- 1 (a - 4))}{a - 4}$

Divide $2 \cdot (- 1)$ by $1$ .

$2 \cdot (- 1)$

Multiply $2$ by $- 1$ .

$- 2$