s2-3s+2=(s-2)(s-1).
(4s2-3s+5)/((s-1)2(s-2))=A/(s-1)+B/(s-1)2+C/(s-2),
4s2-3s+5=As2-3As+2A+Bs-2B+Cs2-2Cs+C,
(1) A+C=4, so C=4-A, (2) -3A+B-2C=-3, (3) 2A-2B+C=5.
2(2)+(3)=-4A-3C=-1, 4A+3C=1
4A+3(4-A)=1,
4A+12-3A=1,
A=-11, C=15, 2A-2B+C=-22-2B+15=5,
2B=-12, B=-6.
(4s2-3s+5)/((s-1)(s2-3s+2))=-11/(s-1)-6/(s-1)2+15/(s-2).
ℒ{eattn}=n!/(s-a)n+1; when a=n=1, ℒ{ett}=1/(s-1)2.
ℒ-1{(4s2-3s+5)/((s-1)(s2-3s+2))}=-11et-6tet+15e2t.