algebra

Plug x in:

$(\sqrt{2+\sqrt{2}})^4+\frac{4}{(\sqrt{2+\sqrt{2}})^4}$ 

Simplify:

$6+4\sqrt2+\frac{4}{6+4\sqrt{2}}$

The fraction's numerator and denominator can both be divided by 2:

$6+4\sqrt2+\frac{2}{3+2\sqrt2}$

I am not sure if this is the simplest form - someone please double check~!!!