Question

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

Answer 1

`x-6`

Explanation:

`color(red)((x^3+8))*(x-2)/(color(blue)(x^2-2x+4))div(color(green)(x^2-4))/(x-6)`

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

`(color(red)((x+2)(x^2-2x+4)))/1xx(x-2)/(color(blue)(x^2-2x+4))xxcolor(green)(x-6)/((x+2)(x-2))`

Now that everything is expressed as factors you may cancel:

`(cancel(x+2)cancel(x^2-2x+4))/1xxcancel(x-2)/(cancel(x^2-2x+4))xx(x-6)/(cancel(x+2)cancel(x-2))`

`=(x-6)`