# Simplifying complex fractions

1. Nov 2, 2008

### russdot

1. The problem statement, all variables and given/known data
$$\frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}$$

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

2. Relevant equations
above

3. 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

2. Nov 2, 2008

### Avodyne

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