# Geometry Question on Rationalizing Denominators

I am looking to check my answer to the problem : $\frac{5\sqrt{2} + 1}{2\sqrt{2} - 1}$. I think it is $3 + \sqrt{2}$.

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That is not the simplification of the given expression. Did you mean$$\frac{5\sqrt{2}+1}{2\sqrt{2}-1}$$ –  DJohnM Sep 21 '13 at 20:40
–  MvG Sep 21 '13 at 20:41
Yes, tht is what I meant. –  IBH Sep 21 '13 at 20:50
Then your simplification is correct... –  DJohnM Sep 21 '13 at 21:32

## 1 Answer

Rationalize the denominator. Multiply it by it conjugate.

$$\frac{5\sqrt{2} + 1}{2\sqrt{2} - 1} = \frac{5\sqrt{2} + 1}{2\sqrt{2} - 1} \cdot \frac{2\sqrt{2} + 1}{2\sqrt{2} + 1} = \frac{(5\sqrt{2} + 1)(2\sqrt{2} + 1)}{(2\sqrt{2})^2 - 1^2} = \frac{21 + 7\sqrt{2}}{7} = 3 + \sqrt{2}$$

So yes, your answer is right.

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