Question

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

Answer 1

Answer:

$\frac{x+2}{x-1}$

Step-by-step explanation:

$\frac{(2x^2+2x-4)}{(2x^2-4x+2)}$

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)

$\frac{(2x^2+2x-4)}{(2x^2-4x+2)}=\frac{(x+2)(2x-2)}{(x-1)(2x-2)}$

2x-2 cancel out

So answer is $\frac{x+2}{x-1}$

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)