# Math Help - single algebraic fraction

1. ## single algebraic fraction

Write each expression as a single algebraic fraction.
(1-xy^-1)^-1

2. $(1-(xy)^{-1})^{-1}$

Remember:
$a^{-1} = \frac{1}{a}$

So:
$(1-(xy)^{-1})^{-1} = \frac{1}{1-(xy)^{-1}} = \frac{1}{1-\frac{1}{xy}}$

Combine 1 and $\frac{1}{xy}$. Remember that $1 = \frac{xy}{xy}$.

$\frac{1}{1-\frac{1}{xy}} = \frac{1}{\frac{xy}{xy}-\frac{1}{xy}} = \frac{1}{\frac{xy - 1}{xy}}$

Now, this expression can be rearranged like this:

$\frac{1}{\frac{xy - 1}{xy}} = 1 \cdot \frac{xy}{xy-1} = \frac{xy}{xy-1}$

3. $xy^{-1}$ can mean $\frac{x}{y}$ too.

4. If you meant $xy^{-1}$ as Wingless pointed out:

$(1-xy^{-1})^{-1}$

$= \frac{1}{1-\frac{x}{y}}$

$= \frac{1}{\frac{y-x}{y}}$

$= 1 \cdot \frac{y}{y-x} = \frac{y}{y-x}$