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

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

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