Processing math: 27%
Home / Aptitude Tests / Further Mathematics / Given that \(\frac{2...
Given that \(\frac{2x}{(x + 6)(x + 3)} = \frac{P}{x + 6} + \...

Given that 2x(x+6)(x+3)=Px+6+Qx+3, find P and Q.

A.

P = 4 and Q = 2

B.

P = 2 and Q = 4

C.

P = 4 and Q = -2

D.

P = -2 and Q = 4

Correct answer is C

2x(x+6)(x+3)=Px+6+Qx+3

2x(x+6)(x+3)=P(x+3)+Q(x+6)(x+6)(x+3)

Comparing equations, we have

2x=Px+3P+Qx+6Q

3P+6Q=0...(1);P+Q=2....(2)

From equation (1), 3P=6QP=2Q

\therefore -2Q + Q = -Q = 2

Q = -2

P = -2Q = -2(-2) = 4

P = 4, Q = -2