evaluate $\frac 1{1+\sqrt2+\sqrt3} + \frac 1{1-\sqrt2+\sqrt3} + \frac 1{1+\sqrt2-\sqrt3} + \frac 1{1-\sqrt2-\sqrt3}$ 
Evaluate $\frac 1{1+\sqrt2+\sqrt3} + \frac 1{1-\sqrt2+\sqrt3} + \frac 1{1+\sqrt2-\sqrt3} + \frac 1{1-\sqrt2-\sqrt3}$

How to evalute this equation without using calculator?

Another way : $$\begin{align}\\&\frac{1}{1+\sqrt 2+\sqrt 3}+\frac{1}{1-\sqrt 2+\sqrt 3}+\frac{1}{1+\sqrt 2-\sqrt 3}+\frac{1}{1-\sqrt 2-\sqrt 3}\\&=\left(\frac{1}{1+\sqrt 2+\sqrt 3}+\frac{1}{1+\sqrt 2-\sqrt 3}\right)+\left(\frac{1}{1-\sqrt 2+\sqrt 3}+\frac{1}{1-\sqrt 2-\sqrt 3}\right)\\&=\frac{1+\sqrt 2-\sqrt 3+1+\sqrt 2+\sqrt 3}{(1+\sqrt 2+\sqrt 3)(1+\sqrt 2-\sqrt 3)}+\frac{1-\sqrt 2-\sqrt 3+1-\sqrt 2+\sqrt 3}{(1-\sqrt 2+\sqrt 3)(1-\sqrt 2-\sqrt 3)}\\&=\frac{2+2\sqrt 2}{(1+\sqrt 2)^2-3}+\frac{2-2\sqrt 2}{(1-\sqrt 2)^2-3}\\&=\frac{2+2\sqrt 2}{2\sqrt 2}+\frac{2-2\sqrt 2}{-2\sqrt 2}\\&=2\end{align}$$
