解方程 (x-5分之x-4)-(x-6分之x-5)=(x-8分之x-7)-(x-9分之x-8)速度
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解:
(x-4)/ (x-5) - (x-5)/(x-6) = (x-7) / (x-8) - (x-8) / (x-9)
对方程两边各自通分:
[(x-4)(x-6) - (x-5)(x-5)] / [(x-5)/(x-6)] = [(x-7)(x-9) - (x-8)(x-8)] / [(x-8)(x-9)]
(x^2-10x+24-x^2+10x-25) / [(x-5)/(x-6)] = [x^2-16x+63 - x^2+16x-64] / [(x-8)(x-9)]
1 / [(x-5)/(x-6)] = 1 / [(x-8)(x-9)]
所以:
(x-5)(x-6)=(x-8)(x-9)
x^2-11x+30=x^2-17x+72
6x=42
x=7
带入原方程:
左边=-1/2
右边=-1/2
左边=右边
∴x=7是原方程的解
(x-4)/ (x-5) - (x-5)/(x-6) = (x-7) / (x-8) - (x-8) / (x-9)
对方程两边各自通分:
[(x-4)(x-6) - (x-5)(x-5)] / [(x-5)/(x-6)] = [(x-7)(x-9) - (x-8)(x-8)] / [(x-8)(x-9)]
(x^2-10x+24-x^2+10x-25) / [(x-5)/(x-6)] = [x^2-16x+63 - x^2+16x-64] / [(x-8)(x-9)]
1 / [(x-5)/(x-6)] = 1 / [(x-8)(x-9)]
所以:
(x-5)(x-6)=(x-8)(x-9)
x^2-11x+30=x^2-17x+72
6x=42
x=7
带入原方程:
左边=-1/2
右边=-1/2
左边=右边
∴x=7是原方程的解
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(x-5分之x-4)-(x-6分之x-5)=(x-8分之x-7)-(x-9分之x-8)
[(x-5)(x-6)]分之1=[(x-8)(x-9)]分之1
(x-5)(x-6)=(x-8)(x-9)
-11x+30=-17x+72
6x=42
x=7
经检验x=7是原方程的解
[(x-5)(x-6)]分之1=[(x-8)(x-9)]分之1
(x-5)(x-6)=(x-8)(x-9)
-11x+30=-17x+72
6x=42
x=7
经检验x=7是原方程的解
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各种方法都很多啊很好那个20及的妙风回答的有问题啊啊啊啊
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(x-5分之x-4)-(x-6分之x-5)=(x-8分之x-7)-(x-9分之x-8)
[1+1/(x-5)]-[1+1/(x-6)]=[1+1/(x-8)]-[1+1/(x-9)]
1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
(x-6-x+5)/[(x-5)(x-6)]=(x-9-x+8)/[(x-8)(x-9)]
-1/[(x-5)(x-6)]=-1/[(x-8)(x-9)]
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
6x=42
x=7
经检验:x=7是原方程的解
[1+1/(x-5)]-[1+1/(x-6)]=[1+1/(x-8)]-[1+1/(x-9)]
1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
(x-6-x+5)/[(x-5)(x-6)]=(x-9-x+8)/[(x-8)(x-9)]
-1/[(x-5)(x-6)]=-1/[(x-8)(x-9)]
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
6x=42
x=7
经检验:x=7是原方程的解
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先两边同加上2
1-(x-5分之x-4)+1-(x-6分之x-5)=1-(x-8分之x-7)+1-(x-9分之x-8)
(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
{1-1/(x-5)}-{1-1/(x-6)}={1- 1/(x-8)}-{1-1/(x-9)}
1/(x-6)-1/(x-5)=1/(x-9)-1/(x-8)
(x-5-x+6)/(x-5)(x-6)=(x-8-x+9)/(x-8)(x-9)
1/(x-5)(x-6)=1/(x-8)(x-9)
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
-11x+17x=72-30
6x=42
x=7
1-(x-5分之x-4)+1-(x-6分之x-5)=1-(x-8分之x-7)+1-(x-9分之x-8)
(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
{1-1/(x-5)}-{1-1/(x-6)}={1- 1/(x-8)}-{1-1/(x-9)}
1/(x-6)-1/(x-5)=1/(x-9)-1/(x-8)
(x-5-x+6)/(x-5)(x-6)=(x-8-x+9)/(x-8)(x-9)
1/(x-5)(x-6)=1/(x-8)(x-9)
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
-11x+17x=72-30
6x=42
x=7
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