Key idea If the rational expression is improper, first divide to get: P(x)Q(x)=S(x)+R(x)Q(x)\frac{P(x)}{Q(x)}=S(x)+\frac{R(x)}{Q(x)}Q(x)P(x)=S(x)+Q(x)R(x) Then resolve only R(x)Q(x)\dfrac{R(x)}{Q(x)}Q(x)R(x) into partial fractions.