If \(\displaystyle \frac{4x + 13}{(x - 2)(x + 1)} = \frac{A}{x - 2} + \frac{B}{x + 1}\) for all x other than 2 and -1, then what are A and B?
cross multipy the R side to get [ a(x+1) + b(x-2) ] / [(x-2)(x+1) ]
Now you can equate the numerators of both sides of the equation
4x+13 = ax+a + bx-2b and now you can equate the 'x' components coefficient and the constant
4 = a+b
13 = a-2b
solve the simple system of red equations to find a = 7 and b = -3