To simplify this expression, we need to combine the terms and factor where possible.

Given expression: X^2 - 1 / (x^2 - 4) * 5x + 10 / (x + 1)

First, let's factor the denominator x^2 - 4 into (x - 2)(x + 2):

= (x^2 - 1) / ((x - 2)(x + 2)) * 5x + 10 / (x + 1)

Next, let's factor the numerator x^2 - 1 into (x - 1)(x + 1):

= ((x - 1)(x + 1)) / ((x - 2)(x + 2)) * 5x + 10 / (x + 1)

Now, simplify the expression by canceling out common factors:

= (x + 1) / (x - 2) * 5x + 10 / (x + 1)
= 5x(x + 1) / (x - 2) + 10 / (x + 1)
= (5x^2 + 5x) / (x - 2) + 10 / (x + 1)
= (5x^2 + 5x + 10(x - 2)) / ((x - 2)(x + 1))
= (5x^2 + 5x + 10x - 20) / ((x - 2)(x + 1))
= (5x^2 + 15x - 20) / ((x - 2)(x + 1))

Therefore, the simplified form of the expression is (5x^2 + 15x - 20) / ((x - 2)(x + 1)).