Question

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

A) x+2/x-1
B) x+2
C) -2
D) x+2/x-2

Answer 1

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)

Answer 2

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

Explanation:

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

Factor top and bottom separately

`2x^2+2x-4`

`2x^2+4x-2x-4`

Make two groups and take out GCf

`2x(x+2)-2(x+2)`

(x+2)(2x-2)

We factor the denominator

`2x^2-4x+2`

`2x^2-2x-2x+2`

Make two groups and take out GCf

`2x(x-1)-2(x-1)`

(x-1)(2x-2)

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

2x-2 cancel out

So answer is
`(x+2)/(x-1)`