Answer
$\displaystyle \frac{x-1}{x+2}$
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 $b$.
$x^{2}-5x+6=(x-3)(x-2)$
$x^{2}-2x-3=(x-3)(x+1)$
... recognize differences of squares:
$x^{2}-1=(x-1)(x+1)$
$x^{2}-4=(x-2)(x+2)$
The problem becomes
$...=\displaystyle \frac{(x-3)(x-2)\cdot(x-1)(x+1)}{(x-3)(x+1)\cdot(x-2)(x+2)}\qquad $... divide out the common factors
$=\displaystyle \frac{\fbox{$(x-3)$}\fbox{$(x-2)$}\cdot(x-1)\fbox{$(x+1)$}}{\fbox{$(x-3)$}\fbox{$(x+1)$}\cdot\fbox{$(x-2)$}(x+2)}\ $
= $\displaystyle \frac{x-1}{x+2}$
