Split 1/x^2-1 into partial fractions

First we need to factorise the denominator into (x-1)(x+1). Now we identify that 1/(x-1)(x+1) is equivalent to A/(x-1) + B/(x+1) and now we solve to find the values of A and B. By simplifying the equivalent expression and collecting coefficients we find that 1 = A(x+1) +B(x-1) which solves to give A=1/2 and B= -1/2.