作业帮解方程： x-5/x-6+x-8/x-9=x-7/x-8+x-6/x-7 过程!
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/05 11:31:21
解方程： x-5/x-6+x-8/x-9=x-7/x-8+x-6/x-7 过程!
解方程： x-5/x-6+x-8/x-9=x-7/x-8+x-6/x-7 过程!
解方程： x-5/x-6+x-8/x-9=x-7/x-8+x-6/x-7 过程!
因为：x-5/x-6+x-8/x-9=x-7/x-8+x-6/x-7,所以：1+1/(x-6)+1+1/(x-9)=1+1/(x-8)+1+1/(x-7)
即：1/(x-6）+1/(x-9)=1/(x-8)+1/(x-7)
所以：1/(x-6)-1/(x-7)=1/(x-8)-1/(x-9)
所以：[(x-7)-(x-6)]/[(x-6)(x-7)]=[(x-9)-(x-8)]/[(x-8)(x-9)]
所以：(x-6)(x-7)=(x-8)(x-9)
即：x^2-13x+42=x^2-17x+72,则：4x=30,解得：x=15/2
每个分式减去1得到
（x-5-x+6）/(x-6) +(x-8-x+9)/(x-9)=(x-7-x+8)/(x-8) +(x-6-x+7)/(x-7)
∴
1/（x-6）+1/(x-9)=1/(x-8) +1/(x-7)
(2x-15)/(x-6)(x-9) =(2x-15)/(x-8)(x-7)
2x-15=0时，成立此时x=7.5
如果2x-1...
全部展开
每个分式减去1得到
（x-5-x+6）/(x-6) +(x-8-x+9)/(x-9)=(x-7-x+8)/(x-8) +(x-6-x+7)/(x-7)
∴
1/（x-6）+1/(x-9)=1/(x-8) +1/(x-7)
(2x-15)/(x-6)(x-9) =(2x-15)/(x-8)(x-7)
2x-15=0时，成立此时x=7.5
如果2x-15≠0
那么((x-6)(x-9) =(x-8)(x-7)
x²-15x+54 =x²-15x+56
显然不成立
所以x=7.5是唯一解
收起
(x-5)/(x-6) + (x-8)/(x-9) = (x-7)/(x-8) + (x-6)/(x-7)
首先，所有分母不为零：
x≠6， 7， 8， 9
(x-5-1+1)/(x-6) + (x-8-1+1)/(x-9) = (x-7-1+1)/(x-8) + (x-6-1+1)/(x-7)
(x-6+1)/(x-6) + (x-9+1)/(x-9) = ...
全部展开
(x-5)/(x-6) + (x-8)/(x-9) = (x-7)/(x-8) + (x-6)/(x-7)
首先，所有分母不为零：
x≠6， 7， 8， 9
(x-5-1+1)/(x-6) + (x-8-1+1)/(x-9) = (x-7-1+1)/(x-8) + (x-6-1+1)/(x-7)
(x-6+1)/(x-6) + (x-9+1)/(x-9) = (x-8+1)/(x-8) + (x-7+1)/(x-7)
1+1/(x-6) + 1+1/(x-9) =1+1/(x-8) + 1+1/(x-7)
1/(x-6) +1/(x-9) =1/(x-8) +1/(x-7)
{(x-6) +(x-9)} / { (x-6) (x-9)} = { (x-8)+ (x-7)} /{ (x-8) (x-7)}
{2x-15} / { (x-6) (x-9)} = { 2x-15 } /{ (x-8) (x-7)}
{2x-15} / { (x-6) (x-9)} - { 2x-15 } /{ (x-8) (x-7)} = 0
(2x-15) { 1/ [ (x-6) (x-9)] - 1 /[ (x-8) (x-7)] = 0
(2x-15) { [ (x-6) (x-9)]- [ (x-8) (x-7)]} / { (x-6) (x-9) (x-8) (x-7) } = 0
(2x-15) { [ (x-6) (x-9)]- [ (x-8) (x-7)]} = 0
(2x-15) { [ x^2-15x+54]- [ x^2-14x+56} = 0
(2x-15) *(-2)= 0
2x-15=0
x=15/2
收起