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

x \(\neq \pm 2\)

Find the value of (P + Q)

A.

\(\frac{3}{2}\)

B.

1

C.

\(\frac{1}{2}\)

D.

0

Correct answer is D

\(\frac{1}{x^2 - 4} = \frac{P}{(x + 2)} + \frac{Q}{(x - 2)}\)

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

Let x = 2

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

I = -4Q 

Q = \(\frac{1}{4}\) 

Let x = -2

I = P(-2  - 2) + Q(-2 + 2)

I = -4p 

P = \(\frac{1}{-4}\) 

PQQ = - \(\frac{1}{4} + \frac{1}{4}\)

= 0