3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解

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3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解
3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解

3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解
令a=(x²+1)/(x+2)
则3a=4/a+4
3a²-4a-4=0
(3a+2)(a-2)=0
a=-2/3,a=2
(x²+1)/(x+2)=-2/3
3x²+3=-2x-4
3x²+2x+7=0
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令(x^2+1)/(x+2)=y,原式化为3y=4/y+4，解得Y=3或者Y=-2/3，(x^2+1)/(x+2)=3时，解得X=3或者X=-1，(x^2+1)/(x+2)=-2/3时无解，同时因为X+2处于分母位置，X不能为-2，综上X=3或者X=-1

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