P = 4 and Q = 2
P = 2 and Q = 4
P = 4 and Q = -2
P = -2 and Q = 4
Correct answer is C
\(\frac{2x}{(x + 6)(x + 3)} = \frac{P}{x + 6} + \frac{Q}{x + 3}\)
\(\frac{2x}{(x + 6)(x + 3)} = \frac{P(x + 3) + Q(x + 6)}{(x + 6)(x + 3)}\)
Comparing equations, we have
\(2x = Px + 3P + Qx + 6Q\)
\(\implies 3P + 6Q = 0 ... (1) ; P + Q = 2 .... (2)\)
From equation (1), \(3P = -6Q \implies P = -2Q\)
\(\therefore -2Q + Q = -Q = 2 \)
\(Q = -2\)
\(P = -2Q = -2(-2) = 4\)
\(P = 4, Q = -2\)