解方程(x+1/x+2)+(x+8/x+9)=(x+2/x+3)+(x+7/x+8) 注:要求用简便方法
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![解方程(x+1/x+2)+(x+8/x+9)=(x+2/x+3)+(x+7/x+8) 注:要求用简便方法](/uploads/image/z/7700-68-0.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B%28x%2B1%EF%BC%8Fx%2B2%29%2B%28x%2B8%EF%BC%8Fx%2B9%29%3D%28x%2B2%EF%BC%8Fx%2B3%29%2B%28x%2B7%EF%BC%8Fx%2B8%29+%E6%B3%A8%EF%BC%9A%E8%A6%81%E6%B1%82%E7%94%A8%E7%AE%80%E4%BE%BF%E6%96%B9%E6%B3%95)
解方程(x+1/x+2)+(x+8/x+9)=(x+2/x+3)+(x+7/x+8) 注:要求用简便方法
解方程(x+1/x+2)+(x+8/x+9)=(x+2/x+3)+(x+7/x+8) 注:要求用简便方法
解方程(x+1/x+2)+(x+8/x+9)=(x+2/x+3)+(x+7/x+8) 注:要求用简便方法
1、移项得
(x+1)/(x+2)-(x+2)/(x+3)=(x+7)/(x+8)-(x+8)/(x+9)
2、化简原式
(x+1)/(x+2)=(x+2-1)/(x+2)=1-1/(x+2)
(x+2)/(x+3)=(x+3-1)/(x+3)=1-1/(x+3)
(x+7)/(x+8)=(x+8-1)/(x+8)=1-1/(x+8)
(x+8)/(x+9)=(x+9-1)/(x+9)=1-1/(x+9)
所以,原式=1/(x+3)-1/(x+2)=1/(x+9)-1/(x+8)
3、通分化简得
-1/【(x+3)*(x+2)】=-1/【(x+9)*(x+8)】
所以,(x+3)*(x+2)=(x+9)*(x+8)
所以,再化简得x*x+5x+6-【x*x+17x+72】=12x-66=0
所以x=-5.5