Rationalize the denominator and simplify.
-$\frac{5 \sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}+3 \sqrt{\mathrm{y}}}$
A) $\frac{5 x-15 \sqrt{x y}}{x-9 y}$
B) $\frac{5 x-15 \sqrt{x y}}{x+3 y}$
C) $\frac{5 x-15 \sqrt{x y}}{x-3 y}$
D) $\frac{5 x-15 \sqrt{x y}}{x+9 y}$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac{5 \sqrt{x}}{\sqrt{x}+3 \sqrt{y}}$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{x}-3 \sqrt{y}$. This results in $\frac{5 \sqrt{x}(\sqrt{x}-3 \sqrt{y})}{(\sqrt{x}+3 \sqrt{y})(\sqrt{x}-3 \sqrt{y})}$, simplifying to $\frac{5x-15\sqrt{xy}}{x-9y}$.

Rationalize the Denominator and Simplify 5xx+3y\frac{5 \sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}+3 \sqrt{\mathrm{y}}}x​+3y​5x​​ A) 5x−15xyx−9y\frac{5 x-15 \sqrt{x y}}{x-9 y}x−9y5x−15xy​​

Rationalize the Denominator and Simplify $\frac{5 \sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}+3 \sqrt{\mathrm{y}}}$ A) $\frac{5 x-15 \sqrt{x y}}{x-9 y}$