Answer
$\displaystyle \frac{x-16}{x-4\sqrt{x}}$
Work Step by Step
We lose the square roots in the numerator by applying the difference of squares formula:
$(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}$
$=a^{2}x-b^{2}y$
$\displaystyle \frac{\sqrt{x}+4}{\sqrt{x}}\color{red}{ \cdot\frac{\sqrt{x}-4}{\sqrt{x}-4} }\qquad$ (rationalize)
$=\displaystyle \frac{(\sqrt{x})^{2}-4^{2}}{\sqrt{x}(\sqrt{x}-4)}$
$=\displaystyle \frac{x-16}{(\sqrt{x})^{2}-4\sqrt{x}}$
$=\displaystyle \frac{x-16}{x-4\sqrt{x}}$
