51问答网 > 解方程 x+1分之x+2-x+2分之x+3=x+3分之x+4-x+4分之x+5

解方程 x+1分之x+2-x+2分之x+3=x+3分之x+4-x+4分之x+5

过程

2025-01-07 02:02:54

推荐回答（2个）

回答1：

(x+2)/(x+1)-(x+3)/(x+2)=(x+4)/(x+3)-(x+5)(x+4)
左边=1+1/(x+1)-1-1/(x+2)=1/(x+1)-1/(x+2)=1/(x+1)(x+2)
右边=1+1/(x+3)-1-1/(x+4)=1/(x+3)-1/(x+4)=1/(x+3)(x+4)
1/(x+1)(x+2)=1/(x+3)(x+4)
即(x+1)(x+2)=(x+3)(x+4)
x^2+3x+2=x^2+7x+12
-10=4x
x=-5/2

回答2：

对就是这样 (x+2)/(x+1)-(x+3)/(x+2)=(x+4)/(x+3)-(x+5)(x+4)
左边=1+1/(x+1)-1-1/(x+2)=1/(x+1)-1/(x+2)=1/(x+1)(x+2)
右边=1+1/(x+3)-1-1/(x+4)=1/(x+3)-1/(x+4)=1/(x+3)(x+4)
1/(x+1)(x+2)=1/(x+3)(x+4)
即(x+1)(x+2)=(x+3)(x+4)
x^2+3x+2=x^2+7x+12
-10=4x
x=-5/2