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

Correct Answer is : P = 4 and Q = -2

Correct Answer is : P = 4 and Q = -2

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WAEC Further Mathematics 2015 Paper

Question : 7

Total: 40

Given that

\frac{2x}{(x+6)(x+3)} = \frac{P}{x+6} + \frac{Q}{x+3}

, find P and Q.

Solution:

Concept:

Use partial fractions by combining the right-hand side and then equating coefficients of like powers of

x

Explanation:

Multiply both sides by

(x+6)(x+3)

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

Expand the right-hand side:

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

Group the

x

terms and constant terms:

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

Equate coefficients of

x

P + Q = 2

...(i)

Equate constant terms:

3P + 6Q = 0

...(ii)

From (ii):

3P = -6Q

, so

P = -2Q

Substitute

P = -2Q

into (i):

-2Q + Q = 2 \Rightarrow -Q = 2 \Rightarrow Q = -2

Then

P = -2(-2) = 4

Hence

P = 4

and

Q = -2

Answer:

Option C:

P = 4

and

Q = -2

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