x-1/2014+x-2/2013+x-3/2012=x-10/2005=+x-11/2004+x-12/2003

Đáp án :

`x=2015`

Giải thích các bước giải :

`(x-1)/(2014)+(x-2)/(2013)+(x-3)/(2012)=(x-10)/(2005)+(x-11)/(2004)+(x-12)/(2003)`

`<=>(x-1)/(2014)+(x-2)/(2013)+(x-3)/(2012)-3=(x-10)/(2005)+(x-11)/(2004)+(x-12)/(2003)-3`

`<=>((x-1)/(2014)-1)+((x-2)/(2013)-1)+((x-3)/(2012)-1)=((x-10)/(2005)-1)+((x-11)/(2004)-1)+((x-12)/(2003)-1)`

`<=>(x-1-2014)/(2014)+(x-2-2013)/(2013)+(x-3-2012)/(2012)=(x-10-2005)/(2005)+(x-11-2004)/(2004)+(x-12-2003)/(2003)`

`<=>((x-1-2014)/(2014)+(x-2-2013)/(2013)+(x-3-2012)/(2012))-((x-10-2005)/(2005)+(x-11-2004)/(2004)+(x-12-2003)/(2003))=0`

`<=>(x-2015)/(2014)+(x-2015)/(2013)+(x-2015)/(2012)-(x-2015)/(2005)-(x-2015)/(2004)-(x-2015)/(2003)=0`

`<=>(x-2015)(1/(2014)+1/(2013)+1/(2012)-1/(2005)-1/(2004)-1/(2003))=0`

Vì `1/(2014)+1/(2013)+1/(2012)-1/(2005)-1/(2004)-1/(2003) ≠ 0`

`=>x-2015=0`

`<=>x=2015`

Vậy `x=2015`

~Chúc bạn học tốt !!!~