A/(x+2)+B/(x+3)
=[A(x+3)+B(x+2)]/(x+2)(x+3)
=[(A+B)x+(3A+2B)]/(x+2)(x+3)
=(3x+5)/(x+2)(x+3)
所以A+B=3
3A+2B=5
所以A=-1,B=4
3A+B=1
所以(3A+B)的2008次方=1