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
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Wolfram Alpha says “False”. – MvG Sep 21 '13 at 20:41
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Yes, tht is what I meant. – IBH Sep 21 '13 at 20:50
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Then your simplification is correct... – DJohnM Sep 21 '13 at 21:32
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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.
Stefan4024
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