Answer
$\displaystyle \frac{x+3}{x-2}$
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:
... factor $x^{2}+bx+c $ by searching for two factors of $c$ whose sum is $b$.
$x^{2}+5x+6=(x+3)(x+2)$
$x^{2}+x-6=(x+3)(x-2)$
$x^{2}-x-6=(x-3)(x+2)$
... recognize differences of squares:
$x^{2}-9=(x-3)(x+3)$
The problem becomes
$...=\displaystyle \frac{(x+3)(x+2)\cdot(x-3)(x+3)}{(x+3)(x-2)\cdot(x-3)(x+2)}\qquad $... divide out the common factors
$=\displaystyle \frac{\fbox{$(x+3)$}\fbox{$(x+2)$}\cdot\fbox{$(x-3)$}(x+3)}{\fbox{$(x+3)$}(x-2)\cdot\fbox{$(x-3)$}\fbox{$(x+2)$}}\qquad $
= $\displaystyle \frac{x+3}{x-2}$
