If \(\frac{2}{x - 3} - \frac{3}{x - 2}\) is equal to \(\frac{p}{(x - 3)(x - 2)}\), find p
A. -x - 5
B. -(x + 3)
C. 5x - 13
D. 5 - x
Correct Answer: D
Explanation
\(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\)
\(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)
= \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)
\(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\)
p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2)
p = -x + 5 or p = 5 - x
