Question

2x/（x²+1）—（x²+1）/x=1 简便方法的

Answer 1

2x/（x²+1）—（x²+1）/x=1

设 t= x/(x^2+1)

2t - 1/t =1

2t^2 -t -1=0

(2t +1)(t-1)=0

t= -1/2 或者t=1

t=-1/2时, x/(x^2+1)= -1/2, x^2 + 2x +1=0, x= -1

t=1 时,x/(x^2 +1) =1, x^2 -x +1=0 无解.

x= -1