解分式方程：x²+ x分之7+ x²-x分之1= x²-1分之6

题目

解分式方程：x²+ x分之7+ x²-x分之1= x²-1分之6

答案

7/(x²+x)+ 1/(x²-x)= 6/(x²-1)
7/[x(x+1)]+1/[x(x-1)]-6/[(x+1)(x-1)]=0
[7(x-1)+(x+1)-6x]/[x(x+1)(x-1)]=0
即 7(x-1)+(x+1)-6x=0
7x+x-6x-6=0
2x=6
x=3