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I haven't used my algebra skills much for years and they seem to have atrophied significantly!

I'm having real trouble working out how to re-arrange a formula I've come across to get $x$ by itself on the left hand side. It looks like this:

$\frac{x}{\sqrt{A^{2}-x^{2}}}=\frac{B+\sqrt{C+Dx}}{E+\sqrt{F+G\sqrt{A^{2}-x^{2}}}}$

I've tried every method I can remember but I can't get rid of those pesky square roots!

Any ideas?

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    I've had Mathematica churning away at isolating $x$ for a few minutes now—since Mathematica didn't isolate the variable in a few seconds, I'm guessing that isolating it is not at all simple.2011-03-13

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I would start by multiplying the numerator and denomenator on the right by $E-\sqrt{F+G\sqrt{A^2-x^2}}$: $\frac{x}{\sqrt{A^2 - x^2}} = \frac{\left(B + \sqrt{C + Dx}\right)\left(E - \sqrt{F + G\sqrt{A^2 - x^2}}\right)}{E^2-F+G\sqrt{A^2 - x^2}}$

It may also help the manipulation to set $y = \sqrt{A^2 - x^2}$ for a while.

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    derp yeah sorry2011-03-13