solve 1/(x^2-4) = A/(x+2) + B/(x-2)?

Question

how do u solve for A and B

Answer 1

1/(x^2 -4) = A/(x+2) + B(x-2)
1/(x+2)(x-2) = A/(x+2) + B(x-2)
1 = A(x-2) + B(x+2)
1 - B(x+2) = A(x-2)
(1- Bx + 2B)/(x-2) = A

solve for B the same way.
(1-Ax -2A)/(x+2) = B
There are too many variables to get a number solution with only one equation.

Answer 2

This is a basic problem in partial fractions. The basic way to solve this is to multiply across by (x+2)(x-2)=(x^2-4). this results in

1 = A(x-2) + B(x+2)

Now you can select easy values to use for x like x=2 and x=-2 and substitute them into the above expression.

Case x=2 yields,
1 = A(2-2) + B(2+2) so B=1/4

Case x=-2 yields
1 = A(-2-2) + B(-2+2) so A=-1/4

You can easily verify these answers by considering the RHS of your problem and using the values above and finding a common denominator.