Need to show that $\displaystyle \frac{\frac{1}{x}-\frac{1}{a}}{x-a} = -\frac{1}{ax}$.

Basically, I'll do something like $\displaystyle \left(\frac{1}{x}-\frac{1}{a}\right)\frac{1}{x-a}$, and manipulate it in several different ways, all of which are far more complicated than the simplified form, like $\displaystyle \frac{a-x}{ax^2-a^2x}$. What's the trick here?