There are numbers A and B for which A/(x - 1) + B/(x + 1) = (x + 3)/(x^2 - 1) for every number x other than 1 and -1. Find .A - B.
+2666 We have the equation \({A \over (x - 1)} + {B \over (x + 1)} = {(x + 3) \over (x^2 - 1)}\)
Multiply by \(x^2 -1\): \(A(x+1) + B(x-1) = x + 3\)
From this, we know that \(A + B = 1\) and \(A - B = 3\), so \(A - B = \color{brown}\boxed{3}\)
+2666 We have the equation \({A \over (x - 1)} + {B \over (x + 1)} = {(x + 3) \over (x^2 - 1)}\)
Multiply by \(x^2 -1\): \(A(x+1) + B(x-1) = x + 3\)
From this, we know that \(A + B = 1\) and \(A - B = 3\), so \(A - B = \color{brown}\boxed{3}\)
