Simplify 5+(a+4)/(a-4)

$5 + \frac{a + 4}{a - 4}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{a - 4}{a - 4}$ .

$\frac{5 (a - 4)}{a - 4} + \frac{a + 4}{a - 4}$

Combine the numerators over the common denominator.

$\frac{5 (a - 4) + a + 4}{a - 4}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 a + 5 \cdot - 4 + a + 4}{a - 4}$

Multiply $5$ by $- 4$ .

$\frac{5 a - 20 + a + 4}{a - 4}$

Add $5 a$ and $a$ .

$\frac{6 a - 20 + 4}{a - 4}$

Add $- 20$ and $4$ .

$\frac{6 a - 16}{a - 4}$

Factor $2$ out of $6 a - 16$ .

Factor $2$ out of $6 a$ .

$\frac{2 (3 a) - 16}{a - 4}$

Factor $2$ out of $- 16$ .

$\frac{2 (3 a) + 2 (- 8)}{a - 4}$

Factor $2$ out of $2 (3 a) + 2 (- 8)$ .

$\frac{2 (3 a - 8)}{a - 4}$