To solve the given equation, we first need to find a common denominator for all the fractions. In this case, the common denominator will be x^2 - 1 = (x - 1)(x + 1).

So, we rewrite the equation as:

(x^2 - 4)/(x^2 - 1) + (5(x + 1))/((x - 1)(x + 1)) = (6)/(x^2 - 1)

Now, let's simplify the fractions:

((x + 2)(x - 2))/((x - 1)(x + 1)) + (5(x + 1))/((x - 1)(x + 1)) = 6/(x^2 - 1)

Now, combine the fractions:

(x^2 - 4 + 5x + 5)/(x^2 - 1) = 6/(x^2 - 1)

Simplify the numerator:

(x^2 + 5x + 1)/(x^2 - 1) = 6/(x^2 - 1)

Cross multiply to eliminate the denominators:

x^2 + 5x + 1 = 6

Rearrange the equation in standard form:

x^2 + 5x - 5 = 0

Now, you can solve this quadratic equation using quadratic formula or factoring.