Rationalize the denominator and simplify.
-$\frac{2 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}$
A) $\frac{2 x+4 \sqrt{x y}}{x+2 y}$
B) $\frac{2 x+4 \sqrt{x y}}{x-2 y}$
C) $\frac{2 x+4 \sqrt{x y}}{x+4 y}$
D) $\frac{2 x+4 \sqrt{x y}}{x-4 y}$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate $\sqrt{x}+2\sqrt{y}$. This results in $\frac{2\sqrt{x}(\sqrt{x}+2\sqrt{y})}{(\sqrt{x})^2-(2\sqrt{y})^2}$, simplifying to $\frac{2x+4\sqrt{xy}}{x-4y}$.

Rationalize the Denominator and Simplify 2xx−2y\frac{2 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}x​−2y​2x​​ A) 2x+4xyx+2y\frac{2 x+4 \sqrt{x y}}{x+2 y}x+2y2x+4xy​​

Rationalize the Denominator and Simplify $\frac{2 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}$ A) $\frac{2 x+4 \sqrt{x y}}{x+2 y}$