题目

1.已知1/a-1/b=5,则(2a+3ab-2b)/(a-2b-b)的值是
2.若(1-3x)/(x^2-1)=A/(x+1)+B/(x-1),则A= B=
3.已知a,b为实数,且ab=1,设M=a/(a+1)+b/(b+1),N=1/(a+1)+1/(b+1)则MN的大小关系

提问时间：2020-07-13

答案

1) 1/a-1/b=(b-a)/(ab)=5, a-b=-5ab
(2a+3ab-2b)/(a-2ab-b)=(3ab-2*5ab)/(-5ab-2ab)=1
2) A/(x+1)+B/(x-1)=[A(x-1)+B(x+1)]/(x^2-1)
=[(A+B)x+B-A]/(x^2-1) = (1-3x)/(x^2-1)
所以：A+B=-3, B-A=1,
A=-2, B=-1
3) M=a/(a+1)+b/(b+1)= 1-1/(a+1)+1-1/(b+1）＝2-[1/(a+1)+1/(b+1)]
M-N=2-2[1/(a+1)+1/(b+1)]=2-2(a+1+b+1)/[(a+1)(b+1)]
=2-2(a+b+2)/(ab+a+b+1)
=2-2(a+b+2)/(a+b+2)
=2-2=0
所以M=N