To solve this equation, we can first factor the denominator of the last term on the right side:
x^2 - 1 = (x - 1)(x + 1)
Now we can rewrite the equation:
5/(x - 1) - 3/(x + 1) = 15/((x - 1)(x + 1))
Multiplying all terms by (x - 1)(x + 1) to clear the denominators, we get:
5(x + 1) - 3(x - 1) = 15
Expanding the terms:
5x + 5 - 3x + 3 = 15
Combine like terms:
2x + 8 = 15
Subtract 8 from both sides:
2x = 7
Divide by 2:
x = 7/2
Therefore, the solution to the equation is x = 7/2.
To solve this equation, we can first factor the denominator of the last term on the right side:
x^2 - 1 = (x - 1)(x + 1)
Now we can rewrite the equation:
5/(x - 1) - 3/(x + 1) = 15/((x - 1)(x + 1))
Multiplying all terms by (x - 1)(x + 1) to clear the denominators, we get:
5(x + 1) - 3(x - 1) = 15
Expanding the terms:
5x + 5 - 3x + 3 = 15
Combine like terms:
2x + 8 = 15
Subtract 8 from both sides:
2x = 7
Divide by 2:
x = 7/2
Therefore, the solution to the equation is x = 7/2.