Question

What expression is equivalent to 2x^2+2x-4/2x^2-4x+2

Answer 1

`\large\boxed{(2x^2+2x-4)/(2x^2-4x+2)=(x+2)/(x-1)}`

Explanation:

`(2x^2+2x-4)/(2x^2-4x+2)=(2(x^2+x-2))/(2(x^2-2x+1))=(x^2+x-2)/(x^2-2x+1)\\\\=(x^2+2x-x-2)/(x^2-x-x+1)=(x(x+2)-1(x+2))/(x(x-1)-1(x-1))\\\\=((x+2)(x-1))/((x-1)(x-1))\qquad\text{cancel}\ (x-1)\\\\=(x+2)/(x-1)`

Answer 2

You need to factor the numerator and denominator...

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

(2x(x+2)-2(x+2))/(2x(x-1)-2(x-1))

((2x-2)(x+2))/((2x-2)(x-1)) so the (2x-2)s cancel out leaving

(x+2)/(x-1)