Find all real solutions to the rational equation 3/(x - 1) - 2/(x + 1) = 1.
Answer and explanation
Correct answer: B. x = 3 and x = -2
- Step 1: Multiply by (x - 1)(x + 1): 3(x + 1) - 2(x - 1) = x^2 - 1. Step 2. 3x + 3 - 2x + 2 = x^2 - 1 => x + 5 = x^2 - 1. Step 3. x^2 - x - 6 = 0 => (x - 3)(x + 2) = 0. Step 4. Roots are x = 3 and x = -2, neither of which makes denominators zero. Answer: x = 3 and x = -2. Why not the others: x = 1 and x = -1 are excluded domain values.
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