If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x -
FURTHER MATHEMATICS
WAEC 2014
If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x - 3}\), find the value of (P + Q).
- A. -2
- B. -1
- C. 0
- D. 1
Correct Answer: C. 0
Explanation
\(\frac{x + P}{(x-1)(x-3)} = \frac{Q}{x-1} + \frac{2}{x-3}\)
\(\frac{x + P}{(x-1)(x-3)} = \frac{Q(x-3) + 2(x-1)}{(x-1)(x-3)}\)
Comparing LHS and RHS of the equation, we have
\(x + P = Qx - 3Q + 2x -2\)
\(P = -3Q - 2\)
\(Q + 2 = 1 \implies Q = 1 - 2 = -1\)
\(P = -3(-1) - 2 = 3 - 2 = 1\)
\(P + Q = 1 + (-1) = 0\)
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