问题: 好好学习
-N+2分之N+1和-N+1分之N哪个大?
解答:
(N+1)/(-N+2)-N/(-N+1)
=〔(N+1)(-N+1)-N(-N+2)〕/(-N+2)(-N+1)
=(1-2N)/(-N+2)(-N+1)
定义域: N≠1,2
1.当N>2时,1-2N<0,-N+2<0,-N+1<0, (1-2N)/(-N+2)(-N+1)<0
2.当1<N<2时,1-2N<0,-N+2>0,-N+1<0, (1-2N)/(-N+2)(-N+1)>0
3.当1/2≤N<1时,1-2N<0,-N+2>0,-N+1>0, (1-2N)/(-N+2)(-N+1)≤0
4.当N<1/2时,1-2N>0,-N+2>0,-N+1>0, (1-2N)/(-N+2)(-N+1)>0
所以:
1.当N>2或者1/2<N<1时,(N+1)/(-N+2)<N/(-N+1)
2.当N=1/2时,(N+1)/(-N+2)=N/(-N+1)
3.当1<N<2或者N<1/2时,(N+1)/(-N+2)>N/(-N+1)
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