Answer
False.
Work Step by Step
The given expression is
$\frac{4}{\sqrt{x+y}}=\frac{4\sqrt{x-y}}{x-y}$
Solve the left hand side.
$=\frac{4}{\sqrt{x+y}}$
Multiply the numerator and the denominator by $\sqrt{x+y}$.
$=\frac{4}{\sqrt{x+y}}\cdot \frac{\sqrt{x+y}}{\sqrt{x+y}}$
Use product rule.
$=\frac{4\sqrt{x+y}}{x+y}$
Hence, the statement is false.