解方程:(3x-5)/(x-1)-(2x-5)/(x-2)=1

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/15 00:17:38
解方程:(3x-5)/(x-1)-(2x-5)/(x-2)=1

解方程:(3x-5)/(x-1)-(2x-5)/(x-2)=1
解方程:(3x-5)/(x-1)-(2x-5)/(x-2)=1

解方程:(3x-5)/(x-1)-(2x-5)/(x-2)=1
(3x-5)/(x-1)-(2x-5)/(x-2)=1
(3x-5)(x-2)-(2x-5)(x-1)=(x-1)(x-2)
(3x²-11x+10)-(2x²-7x+5)=x²-3x+2
3x²-11x+10-2x²+7x-5-x²+3x-2=0
-x+3=0
x=3
经检验x=3是原方程的根
所以:原方程的根式x=3

两边同时乘以(x-1)(x-2)再展开化简

x=3

x=3

(3x-5)/(x-1)-(2x-5)/(x-2)=1
(3x-3-2)/(x-1)-(2x-4-1)/(x-2)=1
3-2/(x-1)-[2-1/(x-2)]=1
3-2/(x-1)-2+1/(x-2)=1
1-2/(x-1)+1/(x-2)=1
-2/(x-1)+1/(x-2)=0
-2(x-2)+(x-1)=0
-2x+4+x-1=0
-x+3=0
x=3
经检验x=3是方程的解