已知3X+5/(X+2 )(X+3)=A/X+2+B/X+3(A、B是常数),求(3A+B)^2008
问题描述:
已知3X+5/(X+2 )(X+3)=A/X+2+B/X+3(A、B是常数),求(3A+B)^2008
答
3X+5/(X+2 )(X+3)=+2+B/X+3即(3X+5)/(X+2)(X+3)=A(X+3)/(X+2)(X+3)+B(X+2)/(X+2)(X+3)=[A(X+3)+B(X+2)]/(X+2)(X+3)=[(A+B)x+3A+2B]/(X+2)(X+3)∴A+B=3 3A+2B=5解得A=-1 B=43A+B=1(3A+B)^2008=1...