Solve the rational equation: (1/(x-1)) + (2/(x+1)) = 3/(x^2 - 1).

• A. x = 0
• B. x = 2
• C. x = 4/3
• D. x = -4/3

Answer: (C)

When solving a rational equation, look for a common denominator and combine the fractions. The denominator on the right is x^2 − 1, which factors to (x − 1)(x + 1). Rewrite the left side over this same denominator: (x+1)/(x−1)(x+1) + 2(x−1)/(x+1)(x−1) gives (3x − 1)/[(x−1)(x+1)]. Now the equation is (3x − 1)/[(x−1)(x+1)] = 3/[(x−1)(x+1)]. As long as x is not 1 or −1, you can multiply both sides by the common denominator to cancel it, yielding 3x − 1 = 3. This gives x = 4/3. Since this value does not make any denominator zero, it’s valid. Therefore, x = 4/3.