令t=x-2,则x=t+2,展开为t的幂级数即可(2x+1)/(x^2+x-2)=(x+2+x-1)/[(x+2)(x-1)]=1/(x+2)+1/(x-1)=1/(t+4)+1/(t+1)=1/4*1/(1+t/4)+1/(1+t)=1/4[1-t/4+t^2/4^2-t^3/4^3+...]+[1-t+t^2-t^3+...],收敛区间为|t/4|...