Question

How do you simplify `(x^2 - x-20)/(x^2 - 3x-10) times (x^2 +7x+10)/( x^2 +4x - 5)`?

Answer 1

`=(x+4)/(x-1)`

Explanation:

Factorise each expression as far as possible:

`(x^2-x-20)/(x^2-3x-10) xx (x^2+7x+10)/(x^2+4x-5)`

`=((x-5)(x+4))/((x-5)(x+2))xx((x+5)(x+2))/((x+5)(x-1))`

Now cancel any common factors.

`=(cancel((x-5))(x+4))/(cancel((x-5))cancel((x+2)))xx(cancel((x+5))cancel((x+2)))/(cancel((x+5))(x-1))`

`=(x+4)/(x-1)`