How can I re-arrange this equation? 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?

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.
