Rationalize a fraction using conjugates

Question

I need help rationalizing the following expression using a conjugate:

$$\dfrac{1}{\sqrt{3} + \sqrt{2}-\sqrt{5}}$$

I have had no luck rationalizing this expression with a conjugate of the denominator.

Answer 1

You have to multiply by the conjugate of the denominator.

So you would multiply it by:

$\dfrac{\sqrt{3}-\sqrt{2}+\sqrt{5}}{ \sqrt{3}-\sqrt{2}+\sqrt{5}}$

This will give you:

$\dfrac{2\sqrt{30}+4\sqrt{3}+6\sqrt{2}}{24}$