令(x+1)/x^2=y 则x^2/(x+1)=1/y 原方程可化为y-2/y=1 即y^2-y-2=0 (y-2)(y+1)=0 y=2或y= -1 当y=2即(x+1)/x^2=2 则2x^2-x-1=0 (2x+1)(x-1)=0 x1= -1/2 x2=1 当y= -1即(x+1)/x^2= -1 则x^2+x+1=0 判别式小于0,无解.所以原方程的解是 x1= -1/2 x2=1
(x+1)/x^2-2x^2/(x+1)=1用换元法解方程拜托了各位
令(x+1)/x^2=y 则x^2/(x+1)=1/y 原方程可化为y-2/y=1 即y^2-y-2=0 (y-2)(y+1)=0 y=2或y= -1 当y=2即(x+1)/x^2=2 则2x^2-x-1=0 (2x+1)(x-1)=0 x1= -1/2 x2=1 当y= -1即(x+1)/x^2= -1 则x^2+x+1=0 判别式小于0,无解.所以原方程的解是 x1= -1/2 x2=1