Answer
$\displaystyle \frac{x-2}{x-1}$
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 square of a difference: $a^{2}-2ab+b^{2}=(a-b)^{2}$
$x^{2}-2x+1=x^{2}-2(x)(1)+1^{2}=(x-1)^{2}$
$x^{2}-4x+4=x^{2}-2(x)(2)+2^{2}=(x-2)^{2}$
Also, use : $X^{3}=X\cdot X^{2}$
The problem becomes
$...=\displaystyle \frac{(x-2)(x-2)^{2}\cdot(x-1)^{2}}{(x-1)(x-1)^{2}\cdot(x-2)^{2}}\qquad$ ... divide out the common factors
$=\displaystyle \frac{(x-2)\fbox{$(x-2)^{2}$}\cdot\fbox{$(x-1)^{2}$}}{(x-1)\fbox{$(x-1)^{2}$}\cdot\fbox{$(x-2)^{2}$}}$
= $\displaystyle \frac{x-2}{x-1}$
