How to solve this equation with square roots and fractions? A problem in Optics comes down to this equation:
Given that $A$, $B$, $C$ and $D$ are all real positive numbers, $-1 \lt x \lt 1$ and $-1 \lt \sqrt{C} x \lt 1$
$$\frac{Ax}{\sqrt{1 - x^2}} + \frac{Bx}{\sqrt{1 - Cx^2}} = D$$
How to solve this kind of equation?

You multiply by the product of the denominators and square the result.  That will get you down to one square root, which you can isolate and square again.  Unfortunately, that gives you an eighth degree equation unless there is cancellation.  You can do numeric root finding on the original.
