Simplify by rationalizing the denominator.
-$\frac { \sqrt { 405 x } } { x + \sqrt { y } }$
A) $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x - y }$
B) $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x ^ { 2 } - y }$
C) $\frac { 9 x \sqrt { 5 x } + 9 \sqrt { 5 x y } } { x ^ { 2 } - y ^ { 2 } }$
D) $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x ^ { 2 } - y ^ { 2 } }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, $x - \sqrt{y}$. This results in the denominator being $x^2 - y$, and the numerator becomes $9x\sqrt{5x} - 9\sqrt{5xy}$.

Simplify by Rationalizing the Denominator 405xx+y\frac { \sqrt { 405 x } } { x + \sqrt { y } }x+y​405x​​

Simplify by Rationalizing the Denominator $\frac { \sqrt { 405 x } } { x + \sqrt { y } }$