Answer
$\displaystyle \frac{x^{2}+3x+9}{3x}$
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:
... recognize a difference of cubes, $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$
$x^{3}-8=x^{3}-2^{3}=(x-2)(x^{2}+3x+9)$
... recognize differences of squares:
$x^{2}-4=(x-2)(x+2)$
The problem becomes
$...=\displaystyle \frac{(x-2)(x^{2}+3x+9)\cdot(x+2)}{(x-2)(x+2)\cdot 3x}\qquad$ ... divide out the common factors
$=\displaystyle \frac{\fbox{$(x-2)$}(x^{2}+3x+9)\cdot\fbox{$(x+2)$}}{\fbox{$(x-2)$}\fbox{$(x+2)$}\cdot 3x}$
= $\displaystyle \frac{x^{2}+3x+9}{3x}$
