作业帮解方程1/(x-6)+1/(x-11)=1/(x-7)+1/(x-12)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/07 11:21:52
解方程1/(x-6)+1/(x-11)=1/(x-7)+1/(x-12)
解方程1/(x-6)+1/(x-11)=1/(x-7)+1/(x-12)
解方程1/(x-6)+1/(x-11)=1/(x-7)+1/(x-12)
1/(x-6)+1/(x-11)=1/(x-7)+1/(x-12)
(x-11)(x-7)(x-12)+(x-6)(x-7)(x-12)=(x-6)(x-11)(x-12)+(x-6)(x-11)(x-7)
(x-11+x-6)(x-7)(x-12)=(x-6)(x-11)(x-12+x-7)
(2x-17)(x-7)(x-12)=(x-6)(x-11)(2x-19)
(2x-17)(x^2-19x+84)=(2x-17-2)(x^2-17x+66)
(2x-17)(x^2-17x+66-2x+18)=(2x-17-2)(x^2-17x+66)
(2x-17)(x^2-17x+66)-(2x-18)(2x-17)=(2x-17)(x^2-17x+66)-2(x^2-17x+66)
2(x-9)(2x-17)=2(x^2-17x+66)
2x^2-35x+153=x^2-17x+66
x^2-18x+87=0
无实数解.
没有实根，只有两个虚根9+i*（根号6）和9-i*（根号6）
1/(x-6)-1/(x-7)=1/(x-12)-1/(x-11)
[(x-7)-(x-6)]/(x-6)(x-7)]=[(x-11)-(x-12)]/(x-11)(x-12)
-1/(x-6)(x-7)]=1/(x-11)(x-12)
-(x-11)(x-12)=(x-6)(x-7)
-x²+23x-132=x²-13x+42
x...
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1/(x-6)-1/(x-7)=1/(x-12)-1/(x-11)
[(x-7)-(x-6)]/(x-6)(x-7)]=[(x-11)-(x-12)]/(x-11)(x-12)
-1/(x-6)(x-7)]=1/(x-11)(x-12)
-(x-11)(x-12)=(x-6)(x-7)
-x²+23x-132=x²-13x+42
x²-18x+77=0
(x-7)(x-11)=0
x=7或x=11
经检验：x=7或x=11是增根
∴方程无解
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