What should be added to \frac{1}{(x-2)(x-4)} to get \frac{2x-5}{(x^{2}-5x+6)(x-4)}?
- A. \frac{1}{(x^{2}-7x+12)} ✓
- B. \frac{1}{(x^{2}+7x+12)}
- C. \frac{1}{(x^{2}-7x-12)}
- D. \frac{1}{(x^{2}+7x-12)}
Correct Answer: A. \frac{1}{(x^{2}-7x+12)}
Explanation
Let the term be y. We have \frac{1}{(x-2)(x-4)} + y = \frac{2x-5}{(x-2)(x-3)(x-4)}. Solving for y: y = \frac{2x-5 - (x-3)}{(x-2)(x-3)(x-4)} = \frac{x-2}{(x-2)(x-3)(x-4)} = \frac{1}{(x-3)(x-4)} = \frac{1}{x^2-7x+12}.
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