Rationalize the denominator and then simplify.

Question

Rationalize the denominator and then simplify. ​  ​

Quizplus · Accepted Answer

We can rationalize the denominator  by multiplying both the numerator and denominator by $\sqrt{5}-\sqrt{2}$. This gives us:
\begin{align*}
\frac{3\sqrt{5}+5\sqrt{2}}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}&=\frac{3\sqrt{5}+5\sqrt{2}}{5-2}\
&=\frac{3\sqrt{5}+5\sqrt{2}}{3}.
\end{align*}
Hence, the simplified expression is $\frac{3\sqrt{5}+5\sqrt{2}}{3}$. The correct choice is $\boxed{	extbf{(C)}}$.

Rationalize the Denominator and Then Simplify