换元法解分式方程(x²-2)/(x+3)-(6x+18)/(x²-2)+1=0
问题描述：
换元法解分式方程(x²-2)/(x+3)-(6x+18)/(x²-2)+1=0
答
令(x^2-2)/(x+3)=a则(6x+18)/(x^2-2)=6/a方程改写为a-6/a+1=0a^2+a-6=0(a-2)(a+3)=0a=2 or -3a=2时,(x^2-2)/(x+3)=2x^2-2=2x+6x^2-2x-8=0(x-4)(x+2)=0x=4 or -2a=-3时,(x^2-2)/(x+3)=-3x^2-2=-3x-9x^2+3x+7=0derta=9...