Answer
$\frac{2(x + 1)}{(x + 4)^2}$
Restriction: $x \ne -4, 4$
Work Step by Step
Factor all expressions in the original exercise:
$\frac{2(x - 4)}{(x + 4)(x - 4)} \bullet \frac{(x + 4)(x + 1)}{(x + 4)(x + 4)}$
Rewrite as a single fraction:
$\frac{2(x - 4)(x + 4)(x + 1)}{(x + 4)(x - 4)(x + 4)(x + 4)}$
Cancel common factors in the numerator and denominator:
$\frac{2(x + 1)}{(x + 4)^2}$
Restrictions on $x$ occur when the value of $x$ makes the denominator equal $0$, which means that the denominator becomes undefined.
Set the factors in the denominators equal to $0$ to find restrictions:
First factor:
$x + 4 = 0$
Subtract $4$ from each side of the equation:
$x = -4$
Second factor:
$x - 4 = 0$
Add $4$ to each side of the equation:
$x = 4$
Restriction: $x \ne -4, 4$
