How do you simplify (x^3+8)*(x-2)/(x^2-2x+4)div(x^2-4)/(x-6)?

Sep 27, 2016

$x - 6$

Explanation:

$\textcolor{red}{\left({x}^{3} + 8\right)} \cdot \frac{x - 2}{\textcolor{b l u e}{{x}^{2} - 2 x + 4}} \div \frac{\textcolor{g r e e n}{{x}^{2} - 4}}{x - 6}$

In algebraic fractions you want to factorize as much as possible.

$\frac{\textcolor{red}{\left(x + 2\right) \left({x}^{2} - 2 x + 4\right)}}{1} \times \frac{x - 2}{\textcolor{b l u e}{{x}^{2} - 2 x + 4}} \times \frac{\textcolor{g r e e n}{x - 6}}{\left(x + 2\right) \left(x - 2\right)}$

Now that everything is expressed as factors you may cancel:

$\frac{\cancel{x + 2} \cancel{{x}^{2} - 2 x + 4}}{1} \times \frac{\cancel{x - 2}}{\cancel{{x}^{2} - 2 x + 4}} \times \frac{x - 6}{\cancel{x + 2} \cancel{x - 2}}$

$= \left(x - 6\right)$