Any help would be appreciated... thanks
a2b
__________
ab2 – a1/2 b3
I'd suspect $\displaystyle \frac{a^2b}{ab^2+b^3\sqrt{a}}$
As it happens you can factor $\displaystyle \sqrt{a}$ and $\displaystyle b^2$ from the denominator:
$\displaystyle \frac{a^2b}{b^2\sqrt{a}(\sqrt{a}+b)}$
$\displaystyle b$ and $\displaystyle \sqrt{a}$ cancel:
$\displaystyle \frac{\sqrt{a}}{b(\sqrt{a}+b)}$
You could then multiply by it's conjugate if you wanted to rationalise the denominator
$\displaystyle \frac{\sqrt{a}}{b(\sqrt{a}+b)} \cdot \frac{b(\sqrt{a}-b)}{b(\sqrt{a}-b)}$
$\displaystyle = \frac {b\sqrt{a}(\sqrt{a}-b)}{b^2(a-b^2)}$
And you may cancel a $\displaystyle b$
$\displaystyle = \frac {\sqrt{a}(\sqrt{a}-b)}{b(a-b^2)}$