2x/x^2-9=x-1/x^2-6x+9-1/x+3

2x/x^2-9=x-1/x^2-6x+9-1/x+3
2x/(x+3)(x-3)=(x-1)/(x-3)²-1/(x+3)
两边同乘以(x-3)²(x+3)
2x(x-3)=(x-1)(x+3)-(x-3)²
2x²-6x=x²+2x-3-x²+6x-9
化简为x²-7x+6=0
(x-6)(x-1)=0
解得x=1或6
经检验：x=1或6都是方程的根