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

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

Step 1

Find the common denominator.

Write $a$ as a fraction with denominator $1$ .

$\frac{a}{1} - 4 - \frac{4}{a + 4}$

Multiply $\frac{a}{1}$ by $\frac{a + 4}{a + 4}$ .

$\frac{a}{1} \cdot \frac{a + 4}{a + 4} - 4 - \frac{4}{a + 4}$

Multiply $\frac{a}{1}$ by $\frac{a + 4}{a + 4}$ .

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

Write $- 4$ as a fraction with denominator $1$ .

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

Multiply $\frac{- 4}{1}$ by $\frac{a + 4}{a + 4}$ .

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

Multiply $\frac{- 4}{1}$ by $\frac{a + 4}{a + 4}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $a$ by $a$ .

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

Move $4$ to the left of $a$ .

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

Apply the distributive property.

$\frac{a^{2} + 4 a - 4 a - 4 \cdot 4 - 4}{a + 4}$

Multiply $- 4$ by $4$ .

$\frac{a^{2} + 4 a - 4 a - 16 - 4}{a + 4}$

Step 4

Simplify by adding terms.

Combine the opposite terms in $a^{2} + 4 a - 4 a - 16 - 4$ .

Subtract $4 a$ from $4 a$ .

$\frac{a^{2} + 0 - 16 - 4}{a + 4}$

Add $a^{2}$ and $0$ .

$\frac{a^{2} - 16 - 4}{a + 4}$

Subtract $4$ from $- 16$ .

$\frac{a^{2} - 20}{a + 4}$