There are numbers A and B for which

Question

A/(x-1)+ B/(x+1)=(x+2)/(x^2-1)for every number x≠±1. Find B.

Answer 1

multiply through by x^2-1 = (x-1)(x+1) and you have
A(x+1) + B(x-1) = x+2
Ax+A + Bx-B = x+2
(A+B)x + (A-B) = x + 2
If the two polynomials are the same for all values of x, then the coefficients must match.
Now just solve for B in
A+B = 1
A-B = 2

Now review your section on partial fractions. If you get stuck on a problem, next time show what you have tried, so we can see where you went wrong.