题目

解下列方程：3y+5/3y-6=1/2+5y-4/2y-4；1/x+4-1/x+7=1/x+3-1/x+6.

提问时间：2020-07-23

答案

(3y+5)/(3y-6)=1/2+(5y-4)/(2y-4)
都乘以6(y-2)得,2(3y+5)=3(y-2)+3(5y-4)
6y+10=3y-6+15y-12
6y-3y-15y=-6-12-10
-12y=-28
y=7/3
经检验是原方程的根.
1/(x+4)-1/(x+7)=1/(x+3)-1/(x+6)
1/(x+6)-1/(x+7)=1/(x+3)-1/(x+4)
[(x+7)-(x+6)]/(x+6)(x+7)=[(x+4)-(x+3)]/(x+3)(x+4)
1/(x+6)(x+7)=1/(x+3)(x+4)
(x+6)(x+7)=(x+3)(x+4)
x²+13x+42=x²+7x+12
13x-7x=12-42
6x=-30
x=-5
经检验是原方程的根.