Rationalize the denominator of $\frac { \sqrt { y } } { 7 - \sqrt { y } }$ and simplify.
A) $\sqrt { y }$
B) $\frac { 7 + y } { 49 - y }$
C) $\frac { 7 \sqrt { y } - y } { 49 - y }$
D) $\frac { 7 \sqrt { y } + y } { 49 + y }$
E) $\frac { 7 \sqrt { y } + y } { 49 - y }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator: $7+\sqrt{y}$. 
\begin{align*}
\frac{\sqrt{y}}{7-\sqrt{y}} &= \frac{\sqrt{y}\cdot(7+\sqrt{y})}{(7-\sqrt{y})\cdot(7+\sqrt{y})}\
&= \frac{\sqrt{y}\cdot(7+\sqrt{y})}{49-y}\
&= \frac{7\sqrt{y}+y}{49-y}
\end{align*} 
Therefore, the best choice is $\boxed{\text{(E)}}$.

Rationalize the Denominator Of y7−y\frac { \sqrt { y } } { 7 - \sqrt { y } }7−y​y​​

Rationalize the Denominator Of $\frac { \sqrt { y } } { 7 - \sqrt { y } }$