Solve into partial fraction for 1/(x^2 - 1)

Question

Solve into partial fraction for \(\frac{1}{x^2- 1}\)

Answer 1

Let \(\frac{1}{x^2- 1}\)

1 = A(x – 1) + B(x + 1) … (2)

Put x = 1 in (2) we get

1 = 0 + B(1 + 1)

1 = B(2)

B = \(\frac{1}{2}\)

Put x = -1 in (2) we get

1 = A(-1 – 1) + B(-1 + 1)

1 = -2A + 0

A = \(\frac{-1}{2}\)

Using A = \(\frac{-1}{2}\), B = \(\frac{1}{2}\) in (1) we get