Write each expression as a single algebraic fraction.
(1-xy^-1)^-1
$\displaystyle (1-(xy)^{-1})^{-1}$
Remember:
$\displaystyle a^{-1} = \frac{1}{a}$
So:
$\displaystyle (1-(xy)^{-1})^{-1} = \frac{1}{1-(xy)^{-1}} = \frac{1}{1-\frac{1}{xy}}$
Combine 1 and $\displaystyle \frac{1}{xy}$. Remember that $\displaystyle 1 = \frac{xy}{xy}$.
$\displaystyle \frac{1}{1-\frac{1}{xy}} = \frac{1}{\frac{xy}{xy}-\frac{1}{xy}} = \frac{1}{\frac{xy - 1}{xy}}$
Now, this expression can be rearranged like this:
$\displaystyle \frac{1}{\frac{xy - 1}{xy}} = 1 \cdot \frac{xy}{xy-1} = \frac{xy}{xy-1}$