Answer
$-\displaystyle \frac{2}{x^{2}+3x}$
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:
$8x+2=2(4x+1)$
$3-x=-(x-3)$
$x^{2}-9=(x+3)(x-3)$
$4x^{2}+x=x(4x+1)$
The problem becomes
$...=\displaystyle \frac{2(4x+1)\cdot[-(x-3)]}{(x+3)(x-3)\cdot x(4x+1)}\qquad$ ... divide out the common factors
$=\displaystyle \frac{-2\fbox{$(4x+1)$}\cdot\fbox{$(x-3)$}}{(x+3)\fbox{$(x-3)$}\cdot x\fbox{$(4x+1)$}}\qquad$
$=\displaystyle \frac{-2}{(x+3)x}$
= $-\displaystyle \frac{2}{x^{2}+3x}$
