Home » Find P if (frac{x – 3}{(1 – x)(x + 2)}) = (frac{p}{1 – x}) +…

Find P if (frac{x – 3}{(1 – x)(x + 2)}) = (frac{p}{1 – x}) +…

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 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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