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: Option C
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)