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Given that \(\frac{3x + 4}{(x - 2)(x + 3)}≡\frac{P}{x ...

Given that 3x+4(x2)(x+3)Px+3+Qx2,find the value of Q

A.

2

B.

-2

C.

1

D.

-1

Correct answer is A

3x+4(x2)(x+3)Px+3+Qx2

3x+4(x2)(x+3)=P(x2)+Q(x+3)(x2)(x+3)

=3x+4=P(x2)+Q(x+3)

=3x+4=Px2P+Qx+3Q

=3x+4=Px+Qx2P+3Q

=3x+4=(P+Q)x2P+3Q

Equating x and the constants

P+Q=3------(i)

2P+3Q=4-------(ii)

From equation (i)

P=3-Q------(iii)

Substitute (3-Q) for P inequation (ii)

=-2(3-Q)+3Q=4

=-6+2Q+3Q=4

=-6+5Q=4

=5Q=4+6

=5Q=10

∴Q=105=2