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.
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.