Answer
$x^{2}-y^{2}$
Work Step by Step
Step by step multiplication of rational expressions:
1. Factor completely what you can
2. Reduce (divide) numerators and denominators by common factors.
3. Multiply the remaining factors in the numerators and
multiply the remaining factors in the denominators. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$
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Factor what we can:$x$
$ x^{2}-y^{2}=(x+y)(x-y)\qquad$ ... a difference of squares.
$x^{2}+xy=x(x+y)$
The problem becomes
$...=\displaystyle \frac{(x+y)(x-y)\cdot x(x+y)}{x\cdot(x+y)}\qquad$ ... divide out the common factors
$=\displaystyle \frac{\fbox{$(x+y)$}(x-y)\cdot\fbox{$x$}(x+y)}{\fbox{$x$}\cdot\fbox{$(x+y)$}}\qquad$
$= \displaystyle \frac{(x+y)(x-y)}{1}$
$=(x+y)(x-y)$
= $x^{2}-y^{2}$
