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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\)
\(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)
= \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)
\(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\)
p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2)
p = -x + 5 or p = 5 - x
Source: Myschool Past Questions Archive (Record #36979)