Answer
$$ \frac{4x-9y}{4x}$$
Work Step by Step
First, we must recall the rule:
$$ a^{-b} = \frac{1}{a^b}$$
This gives:
$$ \frac{ \frac{9}{x}-\frac{5}{x-y}}{ \frac{4}{x-y}}$$
We multiply by the least common denominator in the numerator to find:
$$ \frac{ \frac{9(x-y)}{x(x-y)}-\frac{5x}{x(x-y)}}{ \frac{4x}{x(x-y)}}$$
This simplifies to:
$$ \frac{\frac{4x-9y}{x(x-y)}}{\frac{4x}{x(x-y)}}$$
We simplify to find:
$$ \frac{4x-9y}{4x}$$
