Hello, everybody. Currently, I'm learning how to simplify rational expressions. I have the gist of it all, but there's one particular problem that's stumped me. Here it is:

$\displaystyle

\frac {\frac {a}{1 - a} + \frac {1 + a}{a}}{ \frac {1 - a}{a} + \frac{a}{1 + a}}

$

The answer which I've gotten is the following:

$\displaystyle

\frac {(a^2+1)^2}{(-1)(a-1)(a+1)}

$

However, I checked the answer on Mathway.com and it says it's the following:

$\displaystyle

\frac {-a^3+a^2+1}{-a+1}

$

I'm not sure why I'm not getting the answer correct, as I feel I'm doing all the right steps, but surely someone here would know much better than I would. :] I appreciate any help very much.

Colton