If frac 2 x - 3 - frac 3 x - 2 is equal to frac... - WAEC Mathematics 2014 Question
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
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Correct Option: D
(\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
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