已知a.b为实数,且ab=1,a≠1设M=a/(a+1)+b(b+1),N=1/(a+1)+1/(b+1),求M-N的值

已知a.b为实数,且ab=1,a≠1设M=a/(a+1)+b(b+1),N=1/(a+1)+1/(b+1),求M-N的值
已知a.b为实数,且ab=1,a≠1
设M=a/(a+1)+b(b+1),N=1/(a+1)+1/(b+1),求M-N的值

已知a.b为实数,且ab=1,a≠1设M=a/(a+1)+b(b+1),N=1/(a+1)+1/(b+1),求M-N的值
根据题目的结构,感觉M应该是：M=a/(a+1)+b/(b+1)
M-N=a/(a+1)+b/(b+1)-[1/(a+1)+1/(b+1)]
=a/(a+1)+b/(b+1)-1/(a+1)-1/(b+1)
=(a-1)/(a+1)+(b-1)/(b+1)
=(a-1)(b+1)/[(a+1)(b+1)]+(b-1)(a+1)/[(a+1)(b+1)]
=(ab+a-b-1+ab+b-a-1)/(ab+a+b+1)
=2(ab-1)/(ab+a+b+1)
∵ab=1
∴M-N=0