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: Option 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