题目

方程：x+1分之x+2-x+3分之x+4=x+5分之x+6-x+7分之x+8

提问时间：2020-10-03

答案

x+1分之x+2-x+3分之x+4=x+5分之x+6-x+7分之x+8
4/3x+6=12/35x+14
(140/105-36/105)x=8
x=8*105/104
x=105/13


x+1分之x+2-x+3分之x+4=x+5分之x+6-x+7分之x+8
(x+2)/(x+1)-(x+4)/(x+3)=(x+6)/(x+5)+(x+8)/(x+7)
1+1/(x+1)-1-1/(x+3)=1+1/(x+5)+1-1/(x+7)
1/(x+1)-1/(x+3)=1/(x+5)-1/(x+7)
2/(x+1)(x+3)=2/(x+5)(x+7)
(x+1)(x+3)=(x+5)(x+7)
x^2+4x+3=x^2+12x+35
12x-8x=3-35
8x=-32
x=-4