single algebraic fraction

**comet2000** · August 11th 2008, 12:27 PM

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

**Chop Suey** · August 11th 2008, 12:33 PM

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

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:

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

**wingless** · August 11th 2008, 01:16 PM

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

**Chop Suey** · August 11th 2008, 01:33 PM

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

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

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

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

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

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