x方+3/x-4x/x方+3=3用换元法解

问题描述:

x方+3/x-4x/x方+3=3用换元法解

a=(x²+3)/x
a-4/a=3
a²-3a-4=(a-4)(a+1)=0
(x²+3)/x=4
x²-4x+3=(x-1)(x-3)=0
x=1,x=3
(x²+3)/x=-1
x²+x+3=0
无解
x=1,x=3