Question

How do you simplify `(2x-12)/(x^2-4x+4)- ( x-4)/(x-2)`?

Answer 1

`=-(x^2-8x+20)/(x^2-4x+4)`

Explanation:

`(2x-12)/(x^2-4x+4)-(x-4)/(x-2)`

`=(2(x-6)-(x-4)(x-2))/(x-2)^2`

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

`=(2x-12-x^2+6x-8)/(x-2)^2`

`=-(x^2-8x+20)/(x^2-4x+4)`