解方程(X+2)分之(X+1)+(X-7)分之(x+6)=(x+3)分之(x+2)+(x+6)分之(x-5)
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解决时间 2021-10-02 10:11
- 提问者网友:泪痣哥哥
- 2021-10-01 16:28
解方程(X+2)分之(X+1)+(X-7)分之(x+6)=(x+3)分之(x+2)+(x+6)分之(x-5)
最佳答案
- 二级知识专家网友:末日狂欢
- 2020-08-13 06:52
题目有误,应是 (X+2)分之(X+1)+(X+7)分之(x+6)=(x+3)分之(x+2)+(x+6)分之(x+5)
1-1/(X+2)+1-1/(X+7)=1-1/(x+3)+1-1/(x+6)
1/(X+2)+1/(X+7)=1/(x+3)+1/(x+6)
((x+7)+(x+2))/(x+2)(x+7)=((x+6)+(x+3))/(x+3)(x+6)
(2x+9)/(x^2+9x+14)=(2x+9)/(x^2+9x+18)
(2x+9)(x^2+9x+18)=(2x+9)(x^2+9x+14)
(2x+9)(x^2+9x+18-x^2-9x-14)=0
(2x+9)=0
x=-9/2
经检验x=-9/2是方程的解
1-1/(X+2)+1-1/(X+7)=1-1/(x+3)+1-1/(x+6)
1/(X+2)+1/(X+7)=1/(x+3)+1/(x+6)
((x+7)+(x+2))/(x+2)(x+7)=((x+6)+(x+3))/(x+3)(x+6)
(2x+9)/(x^2+9x+14)=(2x+9)/(x^2+9x+18)
(2x+9)(x^2+9x+18)=(2x+9)(x^2+9x+14)
(2x+9)(x^2+9x+18-x^2-9x-14)=0
(2x+9)=0
x=-9/2
经检验x=-9/2是方程的解
全部回答
- 1楼网友:逐風
- 2020-02-05 16:01
(x+1)^2/x+(x+6)(x+1)/x=(x+2)(x+1)/x+(x+5)(x+1)/x
(x+1)/x*{(x+1+x+6)-(x+2)-(x+5)
=(x+1)/x(0=0
所以x∈r(且x≠0)
:(x+1/x+2)+(x+6/x+7)-{(x+2/x+3)+(x+5/x+6)}
=(1+6-2-5)/x+0
=0/x
所以x∈r(且x≠0)
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