Question

Express 1/(x+1)(x-1) in partial fractions?

Answer 1

Let 1/(x+1)(x-1) = A/(x+1) + B/(x-1)
= ( A(x-1) + B(x+1) )/((x-1)(x+1) )
or
A(x-1) + B(x+1) = 1
let x = 1, 2B = 1 ----> B = 1/2
let x = -1, -2A=1 -----> A = -1/2

so 1/(x+1)(x-1)
= 1/(2(x-1)) + 1/(2(x+1))
or (1/2))(1/(x-1)) + 1/(x+1) )

Answer 2

last two lines should be ...

= 1/(2(x-1)) - 1/(2(x+1))
or (1/2))(1/(x-1)) - 1/(x+1) )