（3x+5)/(x+2)+(3x+26)/(x+9)=(3x+17)/(x+6)+(3x+14)/(x+5) 解方程
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解决时间 2021-11-10 12:58
- 提问者网友：呐年旧曙光
- 2021-11-09 16:47
（3x+5)/(x+2)+(3x+26)/(x+9)=(3x+17)/(x+6)+(3x+14)/(x+5) 解方程
最佳答案
- 五星知识达人网友：逃夭
- 2021-11-09 17:01
解方程（3x+5)/(x+2)+(3x+26)/(x+9)=(3x+17)/(x+6)+(3x+14)/(x+5)
解：[3-1/(x+2)]+[3-1/(x+9)]=[3-1/(x+6)]+[3-1/(x+5)]
故得1/(x+2)+1/(x+9)=1/(x+6)+1/(x+5)
两边分别通分得(2x+11)/(x+2)(x+9)=(2x+11)/(x+6)(x+5)
(2x+11)[(x²+11x+30)-(x²+11x+18)]=12(2x+11)=0
故解得x=-11/2
解：[3-1/(x+2)]+[3-1/(x+9)]=[3-1/(x+6)]+[3-1/(x+5)]
故得1/(x+2)+1/(x+9)=1/(x+6)+1/(x+5)
两边分别通分得(2x+11)/(x+2)(x+9)=(2x+11)/(x+6)(x+5)
(2x+11)[(x²+11x+30)-(x²+11x+18)]=12(2x+11)=0
故解得x=-11/2
全部回答
- 1楼网友：夜风逐马
- 2021-11-09 17:34
（3x+5)/(x+2) = [(3x+6) -1] /(x+2) =3 - 1/(x+2) 后面都类似化简
3- 1/(x+2) + 3 - 1/(x+9) = 3 -1/(x+6) + 3 -1/(x+5)
1/(x+2) + 1/(x+9) = 1/(x+6) + 1/(x+5)
(2x+11)/ (x+2)(x+9) =(2x+11)/ (x+6)(x+5)
2x+11 = 0
x = -5.5
3- 1/(x+2) + 3 - 1/(x+9) = 3 -1/(x+6) + 3 -1/(x+5)
1/(x+2) + 1/(x+9) = 1/(x+6) + 1/(x+5)
(2x+11)/ (x+2)(x+9) =(2x+11)/ (x+6)(x+5)
2x+11 = 0
x = -5.5
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