for future reference, this is an

**expression** (equations have equal signs) ...

order of operations; start by getting a common denominator and combining the two terms in parentheses ...

$\dfrac{\sqrt{y}(x+\sqrt{xy})+\sqrt{y}(x-\sqrt{xy})}{x^2-xy} = \dfrac{2x\sqrt{y}}{x(x-y)} = \dfrac{2\sqrt{y}}{x-y}$

do the multiplication ...

$\dfrac{\sqrt{x}-\sqrt{y}}{2\sqrt{xy}} \cdot \dfrac{2\sqrt{y}}{x-y} = \dfrac{1}{\sqrt{x}(\sqrt{x}+\sqrt{y})} = \dfrac{1}{x+\sqrt{xy}}$

add this to the first term ...

$\dfrac{\sqrt{x}+\sqrt{y}-1}{x+\sqrt{xy}} + \dfrac{1}{x+\sqrt{xy}} = \dfrac{\sqrt{x}+\sqrt{y}}{x+\sqrt{xy}}=\dfrac{ \sqrt{x}+\sqrt{y}}{\sqrt{x}(\sqrt{x}+\sqrt{y})} = \dfrac{1}{\sqrt{x}}$

check it ... make sure I didn't screw something up.