Answer
$4$
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:
$4x-4y=4(x-y)$
$x^{2}+xy=x(x+y)$
$ x^{2}-y^{2}=(x+y)(x-y)\qquad$ ... a difference of squares.
The problem becomes
$...= \displaystyle \frac{4(x-y)\cdot x(x+y)}{x\cdot(x+y)(x-y)}\qquad$ ... divide out the common factors
$= \displaystyle \frac{4\fbox{$(x-y)$}\cdot\fbox{$x$}\fbox{$(x+y)$}}{\fbox{$x$}\cdot\fbox{$(x+y)$}\fbox{$(x-y)$}}$
$= \displaystyle \frac{4}{1} $
= $4$
