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Find P if frac x - 3 1 - x x 2 frac p 1 - x fra... - JAMB Mathematics 1994 Question

Find P if \(\frac{x - 3}{(1 - x)(x + 2)}\) = \(\frac{p}{1 - x}\) + \(\frac{Q}{x + 2}\)
A
\(\frac{-2}{3}\)
B
\(\frac{-5}{3}\)
C
\(\frac{5}{3}\)
D
\(\frac{2}{3}\)
correct option: a

(\frac{x - 3}{(1 - x)(x + 2)}) = (\frac{p}{1 - x}) + (\frac{Q}{x + 2})

Multiply both sides by LCM i.e. (1 - x(x + 2))

∴ x - 3 = p(x + 2) + Q(1 - x)

When x = +1

(+1) - 3 = p(+1 + 2) + Q(1 - 1)

-2 = 3p + 0(Q)

3p = -2

∴ p = (\frac{-2}{3})

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