Answer
$-x$.
Work Step by Step
The given expression is
$=\frac{\frac{7}{x+7}}{\frac{1}{x+7}-\frac{1}{x}}$
Multiply the numerator and the denominator by $x(x+7)$.
$=\frac{x(x+7)}{x(x+7)}\cdot \frac{\frac{7}{x+7}}{\frac{1}{x+7}-\frac{1}{x}}$
Use the distributive property.
$=\frac{x(x+7) \cdot \frac{7}{x+7}}{x(x+7) \cdot\frac{1}{x+7}-x(x+7) \cdot\frac{1}{x}}$
Simplify.
$=\frac{7x}{x-(x+7) }$
$=\frac{7x}{x-x-7 }$
$=\frac{7x}{-7 }$
$=-x$.
