If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x -...

If \(\frac{x + P}{(x - 1)(x - 3)} = \frac{Q}{x - 1} + \frac{2}{x - 3}\), find the value of (P + Q).

\(\frac{x + P}{(x-1)(x-3)} = \frac{Q}{x-1} + \frac{2}{x-3}\)

\(\frac{x + P}{(x-1)(x-3)} = \frac{Q(x-3) + 2(x-1)}{(x-1)(x-3)}\)

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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