Answer
$-x$.
Work Step by Step
The given expression is
$=\frac{\frac{4}{x+4}}{\frac{1}{x+4}-\frac{1}{x}}$
Multiply the numerator and the denominator by $x(x+4)$.
$=\frac{x(x+4)}{x(x+4)}\cdot \frac{\frac{4}{x+4}}{\frac{1}{x+4}-\frac{1}{x}}$
Use the distributive property.
$=\frac{x(x+4) \cdot \frac{4}{x+4}}{x(x+4) \cdot\frac{1}{x+4}-x(x+4) \cdot\frac{1}{x}}$
Simplify.
$=\frac{4x}{x-(x+4) }$
$=\frac{4x}{x-x-4 }$
$=\frac{4x}{-4 }$
$=-x$.
