-2
-1
0
1
Correct answer is C
\(\frac{x + P}{(x-1)(x-3)} = \frac{Q}{x-1} + \frac{2}{x-3}\)
\(\frac{x + P}{(x-1)(x-3)} = \frac{Q(x-3) + 2(x-1)}{(x-1)(x-3)}\)
Comparing LHS and RHS of the equation, we have
\(x + P = Qx - 3Q + 2x -2\)
\(P = -3Q - 2\)
\(Q + 2 = 1 \implies Q = 1 - 2 = -1\)
\(P = -3(-1) - 2 = 3 - 2 = 1\)
\(P + Q = 1 + (-1) = 0\)