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

If x+P(x1)(x3)=Qx1+2x3, find the value of (P + Q)

A.

-2

B.

-1

C.

0

D.

1

Correct answer is C

x+P(x1)(x3)=Qx1+2x3

x+P(x1)(x3)=Q(x3)+2(x1)(x1)(x3)

Comparing LHS and RHS of the equation, we have

x+P=Qx3Q+2x2

P=3Q2

Q+2=1Q=12=1

P=3(1)2=32=1

P+Q=1+(1)=0