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})