How Do You Simplify Complex Fractions with Nested Radicals?

[russdot]

Homework Statement

$$\frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}$$

Should equal $$\left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2}$$

Homework Equations

above

The Attempt at a Solution

I have tried numerous ways of trying to simplify the initial equation to equal the second, but cannot seem to get rid of the multi-term denominator.

What is a good formula/method for reducing a fraction such as this?
Thanks

 

[Avodyne]

When you have a denominator of the form $1-\sqrt{A}$, multiply numerator and denominator by $1+\sqrt{A}$.