Answer:
[tex]\frac{x+2}{x-1}[/tex]
Step-by-step 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
[tex]\frac{2x^2+2x-4}{2x^2-4x+2}[/tex]
= [tex]\frac{2(x+2)(x-1)}{2(x-1)^2}[/tex]
Cancel 2 and factor (x - 1) on numerator/ denominator, leaving
= [tex]\frac{x+2}{x-1}[/tex]
