解分式方程7/x^2+x-3/x-x^2=1+7-x^2/x^2-1

解分式方程7/x^2+x-3/x-x^2=1+7-x^2/x^2-1
解分式方程7/x^2+x-3/x-x^2=1+7-x^2/x^2-1

解分式方程7/x^2+x-3/x-x^2=1+7-x^2/x^2-1
7/(x^2+x) - 3/(x-x^2)=1+ (7-x^2)/(x^2-1)
7/(x^2+x) - 3/(x-x^2)=1+ (1-x^2+6)/(x^2-1)
7/(x^2+x) - 3/(x-x^2)=1-1+6/(x^2-1)
7/(x^2+x) - 3/(x-x^2)=6/(x^2-1)
7/x(x+1) - 3/x(1-x)=6/(x-1)(x+1)
7/x(x+1)+ 3/x(x-1)=6/(x-1)(x+1)
7(x-1)/x(x+1)(x-1)+ 3(x+1)/x(x-1)(x+1)=6x/x(x-1)(x+1)
[7(x-1)+ 3(x+1)]/x(x-1)(x+1)=6x/x(x-1)(x+1)
(10x-4)/x(x-1)(x+1)=6x/x(x-1)(x+1)
(10x-4)/x(x-1)(x+1)-6x/x(x-1)(x+1)=0
(10x-4-6x)/x(x-1)(x+1)=0
(4x-4)/x(x-1)(x+1)=0
(x-1)/x(x-1)(x+1)=0
x=±1,x=0分式无意义
所以方程无解