What is the sum of this power series?

This is the series: $$\sum_{n=1}^\infty \frac{x^{2n}}{(2+\sqrt{2})^n}$$

My problem is that I don't know how to rid of that $(2+\sqrt{2})^{-n}$.

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Hint: consider $t=x^2/(2+\sqrt2)$. –  Did Jan 21 '13 at 18:20

HINT Let $y = \dfrac{x^2}{2+\sqrt{2}}$ and see what happens.
I recommend using the identities $x^{2n}=(x^2)^n$ and $\dfrac{a^n}{b^n}=\left(\dfrac{a}{b}\right)^n$.