Simplify these expressions with radical sign 2 My question is 

1) Rationalize the denominator: 
  $$\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$$

My answer is:
$$\frac{\sqrt{12}+\sqrt{18}-\sqrt{30}}{18}$$
My question is 

2) $$\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}+\frac{1}{\sqrt{2}-\sqrt{3}-\sqrt{5}}$$

My answer is: $$\frac{1}{\sqrt{2}}$$
I would also like to know whether my solutions are right.
Thank you, 

$\begin{eqnarray*}
(\sqrt{2}+\sqrt{3}+\sqrt{5})(\sqrt{12}+\sqrt{18}-\sqrt{30}) & = & (\sqrt{2}+\sqrt{3}+\sqrt{5})(2\sqrt{3}+3\sqrt{2}-\sqrt{2}\sqrt{3}\sqrt{5})\\& = & 12,
\end{eqnarray*}$
if you expand out the terms, so your first answer is incorrect. The denominator should be $12$.
$\begin{eqnarray*}
(\sqrt{2}+\sqrt{3}-\sqrt{5})(\sqrt{2}-\sqrt{3}-\sqrt{5}) & = & (\sqrt{2}-\sqrt{5})^2-\sqrt{3}^2\\& = & 7-2\sqrt{10}-3\\& = & 2\sqrt{2}(\sqrt{2}-\sqrt{5}),
\end{eqnarray*}$
and so when your fractions in the second part are given common denominators, you'll have exactly $\cfrac{1}{\sqrt{2}}$ after cancellation, so your second answer is correct.
Note: In general, if you want to see if two fractions are the same (as in the first problem), cross-multiplication is often a useful way to see it.
