There are numbers A and B for which
A/(x - 1) + B/(x + 1) = (2x + 1)/(x^2 - 1)
for every number $x \neq \pm 1$. Find B.
A/(x - 1) + B/(x + 1) = (A(x+1) + B(x-1))/(x+1)/(x-1) = (2x + 1)/(x^2 - 1)
A(x+1) + B(x-1) = (2x + 1)
(A+B)x + A - B = 2x + 1
A + B = 2
A - B = 1
Can you solve B from here?
=^._.^=
