Find P if \(\frac{x - 3}{(1 - x)(x + 2)}\) = \(\frac{p}{1 - x}\) +...

Mathematics

JAMB 1994

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. \(\frac{2}{3}\)

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Correct Answer: Option A

Explanation

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

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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