Answer:
We can factor out a 4x from the numerator and a 2 from the denominator, which gives:
(4x(x+1)) / 2( x^2 - 1)
We can then factor the denominator further using the difference of squares formula, which gives:
(4x(x+1)) / 2(x+1)(x-1)
Simplifying this expression further, we can cancel out the (x+1) terms in the numerator and denominator, which gives:
2x / (x-1)
Therefore, 4x^2 + 4x / 2x^2 - 2 simplifies to 2x / (x-1).