Answer
$\displaystyle \frac{x+4}{x+2}$
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. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$
---
Factor what we can:
... recognize a square of a sum: $a^{2}+2ab+b^{2}=(a+b)^{2}$
$x^{2}+4x+4=x^{2}+2(x)(2)+2^{2}=(x+2)^{2}$
$x^{2}+8x+16=x^{2}+2(x)(4)+4^{2}=(x+4)^{2}$
Also, use : $X^{3}=X\cdot X^{2}$
The problem becomes
$...=\displaystyle \frac{(x+4)(x+4)^{2}\cdot(x+2)^{2}}{(x+2)(x+2)^{2}\cdot(x+4)^{2}}\qquad$ ... divide out the common factors
$=\displaystyle \frac{(x+4)\fbox{$(x+4)^{2}$}\cdot\fbox{$(x+2)^{2}$}}{(x+2)\fbox{$(x+2)^{2}$}\cdot\fbox{$(x+4)^{2}$}}$
= $\displaystyle \frac{x+4}{x+2}$
