Question

When multiplying 2x-8/x^2-4 times x^2+6x+8/x-4, what are the term(s) that can be cancelled

Answer 1

(x-4) and (x+2) are terms that can be cancelled

Explanation:

we are given

`(2x-8)/(x^2-4)* (x^2+6x+8)/(x-4)`

Firstly, we will factor terms

and then we can cancel common terms

`2x-8=2(x-4)`

`x^2-4=(x-2)(x+2)`

`x^2+6x+8=(x+4)(x+2)`

now, we can replace it

`(2x-8)/(x^2-4)* (x^2+6x+8)/(x-4)=(2(x-4))/((x-2)(x+2))* ((x+2)(x+4))/(x-4)`

now, we can see that

(x-4) and (x+2) are common

so, they will get cancelled

`(2x-8)/(x^2-4)* (x^2+6x+8)/(x-4)=(2)/((x-2))* ((x+4))/(1)`

so, we can see that

(x-4) and (x+2) are terms that can be cancelled