>>101
y = x+1と置く

f(x) = 1/{ (2-y)(-1+3y) } = (1/5) { 1/(2-y) } + (1/5) { 3/(-1+3y) }
= ( 1/10) { 1/(1-(y/2)) } - (3/5) { 1/(1-3y)}

1/(1-x) = Σx^kだから

1/(1-(y/2)) = Σ (y/2)^k
1/(1-3y) = Σ(3y)^k