u^2/(u^2+3u+2)=1+1/(u+1)-4/(u+2)等号左边是用什么方法变成等号右边的u^2/(u^2+3u+2)=1+1/(u+1)-4/(u+2)等号左边是用什么方法变成等号右边的?

Question

u^2/(u^2+3u+2)=1+1/(u+1)-4/(u+2) 等号左边是用什么方法变成等号右边的
u^2/(u^2+3u+2)=1+1/(u+1)-4/(u+2)
等号左边是用什么方法变成等号右边的?

Answer 1

u²/(u²+3u+2)=1+1/(u+1)-4/(u+2) 等号左边是用什么方法变成等号右边的
左边=1-(3u+2)/(u²+3u+2)=1-(3u+2)/(u+1)(u+2)=1-A/(u+1)-B/(u+2)
=1-[A(u+2)+B(u+1)]/(u+1)(u+2)=1-[(A+B)u+2A+B]/(u+1)(u+2)
这是恒等变换,对应项系数应该相等,故有：
A+B=3.(1)；2A+B=2.(2)
两式联立求解,不难求得A=-1；B=4
故u²/(u²+3u+2)=1+1/(u+1)-4/(u+2).