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Given that \(\frac{1}{x^2 - 4} = \frac{p}{(x + 2)} + \fra...

Given that 1x24=p(x+2)+Q(x2)

x ±2

Find the value of (P + Q)

A.

32

B.

1

C.

12

D.

0

Correct answer is D

1x24=P(x+2)+Q(x2)

I = p(x - 2) + Q(x + 2)

Let x = 2

I = P(2 - 2) + Q(2+ 2)

I = -4Q 

Q = 14 

Let x = -2

I = P(-2  - 2) + Q(-2 + 2)

I = -4p 

P = 14 

PQQ = - 14+14

= 0