Find P if \(\frac{x – 3}{(1 – x)(x + 2)}\) = \(\frac{p}{1 – x}\) + \(\frac{Q}{x + 2}\)
-
\(\frac{-2}{3}\)
- \(\frac{-5}{3}\)
- \(\frac{5}{3}\)
- \(\frac{2}{3}\)
The correct answer is: 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 = \(\frac{-2}{3}\)