求证分式x^-1/(1+xy)^-(x+y)^不可能为零
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求证分式x^-1/(1+xy)^-(x+y)^不可能为零
求证分式x^-1/(1+xy)^-(x+y)^不可能为零
求证分式x^-1/(1+xy)^-(x+y)^不可能为零
设(x^2-1)/[(1+xy)^2-(x+y)^2]
=(x-1)(x+1)/[(1+xy)^2-(x+y)^2]
=0
则:x=1,或,-1
x=1时
分母(1+xy)^2-(x+y)^2=(1+y)^2-(1+y)^2=0
x=-1时,
分母(1+xy)^2-(x+y)^2=(1-y)^2-(-1+y)^2=(1-y)^2-(1-y)^2=0
都不可能
所以,分式x^-1/(1+xy)^-(x+y)^不可能为零