\[\frac{f(x)}{(x-\alpha_{1})^{m_{1}}(x-\alpha_{2})^{m_{2}}\cdots(x-\alpha_{n})^{%
m_{n}}}=\frac{f_{1}(x)}{(x-\alpha_{1})^{m_{1}}}+\frac{f_{2}(x)}{(x-\alpha_{2})%
^{m_{2}}}+\cdots+\frac{f_{n}(x)}{(x-\alpha_{n})^{m_{n}}}.\]