Question

解方程x+1/x²-2x²/x+1=1

Answer 1

(x+1)/x²-2x²/(x+1)=1

令y=(x+1)/x²,则x²/(x+1)=1/y,原式可变形为：

y-2/y=1 两边同时乘以y得

y²-2=y

y²-y-2=0

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

y=-1（舍去）或y=2

∴y=2

即(x+1)/x²=2

2x²=x+1

2x²-x-1=0

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

x1=-1/2,x2=1