Question

For which rational expression is -which expression is equivalent to 2x^2+2x-4/2x^2-4x+2

Answer 1

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

Explanation:

Factorise the numerator and denominator

2x² + 2x - 4 ← factor out 2 from each term

= 2(x² + x - 2)

= 2(x + 2)(x - 1) ← in factored form

2x² - 4x + 2 ← factor out 2 from each term

= 2(x² - 2x + 1)

= 2(x - 1)² ← in factored form

Thus

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

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

Cancel 2 and factor (x - 1) on numerator/ denominator, leaving

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