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I'm doing my homework and I'm stuck on this problem: $$ \frac{\frac 1 {\sqrt{a}} + \frac {\sqrt{a}} 2}{\frac 1 {\sqrt{a}} - \frac {\sqrt{a}} 2} $$ I tried playing around with the powers, but failed pretty hard.

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    $\begingroup$ Multiply by $$\frac{\frac{1}{\sqrt a} + \frac{\sqrt a}{2}}{\frac{1}{\sqrt a} + \frac{\sqrt a}{2}}$$ $\endgroup$
    – AlexR
    Oct 8, 2013 at 17:25
  • $\begingroup$ Try to add and subtract fractions in the numerator and denominator. $\endgroup$
    – user35603
    Oct 8, 2013 at 17:26

2 Answers 2

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Expand by $2\sqrt{a}$ and your'e done.

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Multiply above and below by $\sqrt{a}$ to get $\frac{1+ \frac{a}{2}}{1- \frac{a}{2}} = \frac{2+a}{2-a}$.

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