Rationalize the denominator and simplify So the problem I have says rationalize the denominator and simplify.
$$    \frac{ \sqrt{15}}{\sqrt{10}-3}$$
My answer I got was $\frac{5 \sqrt6}{7}$.
Am I doing this wrong or is this the wrong answer I was told it was incorrect?

It seems that you tried multiplying by $\frac{\sqrt{10}}{\sqrt{10}}$. Instead, you should try multiplying by the conjugate and take advantage of difference of squares:
$$
\frac{\sqrt{15}}{\sqrt{10} - 3}
= \frac{\sqrt{15}}{\sqrt{10} - 3} \cdot \frac{\sqrt{10} + 3}{\sqrt{10} + 3}
= \frac{\sqrt{150} + 3\sqrt{15}}{(\sqrt{10})^2 - 3^2}
= 5\sqrt{6} + 3\sqrt{15}
$$
