初高中衔接课程数学自主训练 该题如下1/(x+2)+1/(x+3)=1/(x+1)+1/(x+4)

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初高中衔接课程数学自主训练 该题如下1/(x+2)+1/(x+3)=1/(x+1)+1/(x+4)

初高中衔接课程数学自主训练 该题如下1/(x+2)+1/(x+3)=1/(x+1)+1/(x+4)
初高中衔接课程数学自主训练 该题如下
1/(x+2)+1/(x+3)=1/(x+1)+1/(x+4)

初高中衔接课程数学自主训练 该题如下1/(x+2)+1/(x+3)=1/(x+1)+1/(x+4)
为方便计算,可令t=x+2,则原方程即为:
1/t+1/(t+1)=1/(t-1)+1/(t+2)
通分,方程两边同乘以t(t+1)(t-1)(t+2):
(t^2-1)(t+2)+(t^2-t)(t+2)=(t^2+t)(t+2)+t(t^2-1),化简后即为:
-4t=2,得到t=-0.5
则x=t-2=-2.5

x=-2.5