Simplification of a derivative

I'm in the process of a derivative and I'm having trouble simplifying. Would someone mind helping me out with where to start.

Here is the original problem I was told to differentiate:

$\displaystyle \theta = \frac{1-a\sqrt[3]{t^2}}{1+a\sqrt{t^3}}$

I decided to use the quotient rule and came up with this as the first step:

$\displaystyle \frac{1-at^{\frac{2}{3}}}{ 1+at^{\frac{3}{2}}}$

and then this:

$\displaystyle \frac{(1+at^{\frac{3}{2}})(\frac{-2}{3}at^{\frac{-1}{3}}) - (1-at^{\frac{2}{3}})(\frac{3}{2}at^{\frac{1}{2}})}{(1 +at^{\frac{3}{2}})^2}$

and here is what I multiplied it all out to:

$\displaystyle \frac{\frac{-2}{3}at^\frac{-1}{3} + \frac{-2}{3}a^2t^{\frac{7}{6}} - \frac{3}{2}at^{\frac{1}{2}} - \frac{3}{2}a^2t^{\frac{7}{6}}}{(1+at^{\frac{3}{2}} )^2}$

Now, its been a while and my algebra is rusty so I'm stuck here. What is the first thing you would do to go about simplifying? Thanks in advance.