+980 There are numbers \(A\) and \(B\) for which \(\frac A{x-1}+\frac B{x+1}=\frac{x+2}{x^2-1}\)for every number \(x\neq\pm1\). Find \(A-B\).
+23252 The common denominator is (x + 1)(x - 1)
Multiply each term by this and the equation becomes: A(x + 1) + B(x - 1) = x + 2
Multiplying out: Ax + A + Bx - B = x + 2
Factoring: (A + B)x + (A - B) = x + 2
Setting the X-terms to each other: (A + B)x = x ---> A + B = 1
Setting the constants to each other: A - B = 2
Solving these two equations: A = 1.5 and B = - 0.5
