Simplify 12/(a-4)+(3a)/(4-a)

$\frac{12}{a - 4} + \frac{3 a}{4 - a}$

Simplify terms.

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

$\frac{12}{a - 4} + \frac{3 a}{- 1 (- 4) - a}$

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

$\frac{12}{a - 4} + \frac{3 a}{- 1 (- 4) - (a)}$

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

$\frac{12}{a - 4} + \frac{3 a}{- 1 (- 4 + a)}$

Simplify the expression.

Move a negative from the denominator of $\frac{3 a}{- 1 (- 4 + a)}$ to the numerator.

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

Reorder terms.

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

Combine the numerators over the common denominator.

$\frac{12 - (3 a)}{a - 4}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$\frac{12 - 3 a}{a - 4}$

Factor $3$ out of $12 - 3 a$ .

Factor $3$ out of $12$ .

$\frac{3 (4) - 3 a}{a - 4}$

Factor $3$ out of $- 3 a$ .

$\frac{3 (4) + 3 (- a)}{a - 4}$

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

$\frac{3 (4 - a)}{a - 4}$

Reduce the expression by cancelling the common factors.

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

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

$\frac{3 (- 1 (- 4) - a)}{a - 4}$

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

$\frac{3 (- 1 (- 4) - (a))}{a - 4}$

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

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

Reorder terms.

$\frac{3 (- 1 (a - 4))}{a - 4}$

Cancel the common factor.

$\frac{3 (- 1 (a - 4))}{a - 4}$

Divide $3 \cdot (- 1)$ by $1$ .

$3 \cdot (- 1)$

Multiply $3$ by $- 1$ .

$- 3$