On the transformation of proper fraction into partial fraction sum Q (x) = (x-x1 (x-x2) -- (x-xn), then, r(x)/Q(x)=A1(x-x1)+A2/(x-x2)----+An/x-xn) Where, how to use the undetermined coefficient method to find AI (I = 1,2,3,4, --)

On the transformation of proper fraction into partial fraction sum Q (x) = (x-x1 (x-x2) -- (x-xn), then, r(x)/Q(x)=A1(x-x1)+A2/(x-x2)----+An/x-xn) Where, how to use the undetermined coefficient method to find AI (I = 1,2,3,4, --)

A simple problem is that x1, X2,..., xn are not equal to each other, then the value of R (x) * (x-xk) / Q (x) when x = XK is AK, where k = 1,2,..., n if there are some two or several XK equal cases, such as X1 = x2 = u, then the partial fraction decomposition result should be A1 / (x-u) + A2 / (x-u) ^ 2 corresponding to A1 = (R (x) * (...)