Given that (frac{2x}{(x + 6)(x + 3)} = frac{P}{x + 6} + frac{Q}{x + 3}),…

Given that (frac{2x}{(x + 6)(x + 3)} = frac{P}{x + 6} + frac{Q}{x + 3}), find P and Q.

Correct Answer: Option C

Explanation

(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)