Answer:
[tex]\frac{2x}{x-1}[/tex]
Step-by-step explanation:
[tex]\frac{4x^2+4x}{2x^2-2}[/tex] ← factor numerator and denominator
= [tex]\frac{4x(x+1)}{2(x^2-1)}[/tex] ← cancel 4 and 2 on numerator/denominator by 2
= [tex]\frac{2x(x+1)}{x^2-1}[/tex] ← x² - 1 is a difference of squares
= [tex]\frac{2x(x+1)}{(x-1)(x+1)}[/tex] ← cancel (x + 1) on numerator and denominator
= [tex]\frac{2x}{x-1}[/tex]
