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

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Answer 1 · 2016-09-27T20:38:57

$x-6$

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

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:

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

$=(x-6)$

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