(x+2005)/ (x+2004)+(x+2007)/(x+2006)=(x+2008)/(x+2007)+(x+2004)/(x+2003) 解方程

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/08 17:47:51
(x+2005)/ (x+2004)+(x+2007)/(x+2006)=(x+2008)/(x+2007)+(x+2004)/(x+2003) 解方程

(x+2005)/ (x+2004)+(x+2007)/(x+2006)=(x+2008)/(x+2007)+(x+2004)/(x+2003) 解方程
(x+2005)/ (x+2004)+(x+2007)/(x+2006)=(x+2008)/(x+2007)+(x+2004)/(x+2003) 解方程

(x+2005)/ (x+2004)+(x+2007)/(x+2006)=(x+2008)/(x+2007)+(x+2004)/(x+2003) 解方程
各分式减1,得
1/(x+2004)+1/(x+2006)=1/(x+2007)+1/(x+2003),
通分得(2x+4010)/[(x+2004)(x+2006)]=(2x+4010)/[(x+2003)(x+2007)],
两边的分母不等,
∴2x+4010=0,
x=-2005.
检验知,它是原方程的根.

((x+2004)+1)/(x+2004)+((x+2006)+1)/(x+2006)=((x+2007)+1)/(x+2007)+)((x+2003)+1)/(x+2004)=1/(x+2004)+1/(x+2006)=1/(x+2007)+1/(x+2003) 通分 得到6X=-12030 ∴X=-2005