Hình như để như này : 

\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)

\(\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)=0\)

\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=0\)

\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\right)=0\)

Do \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}>0\Rightarrow x+2015=0\)

\(\Leftrightarrow x=-2015\)

Vậy \(x=-2015\)

cảm ơn bạn

Tìm x, biết: \(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)

Đề như trên có đúng không bạn? ._.

\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+3=0\)

\(\frac{x+1}{2014}+1+\frac{x+2}{2013}+1+\frac{x+3}{2012}+1=0\)

\(\left(\frac{x+1}{2014}+\frac{2014}{2014}\right)+\left(\frac{x+2}{2013}+\frac{2013}{2013}\right)+\left(\frac{x+3}{2012}+\frac{2012}{2012}\right)=0\)

\(\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=0\)

\(\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\right)=0\)

Mà \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}\ne0\)

\(\Rightarrow x+2015=0\)

\(\Rightarrow x=-2015\)

Vậy \(x=-2015\).

Ta có : \(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=-3.\)

\(\Leftrightarrow\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=-3+3\)

\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}=0\)

\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)=0\)

Mà \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\ne0\) nên \(x+2014=0\Leftrightarrow x=-2014\)

Vây \(x=-2014\)

http://h.vn/hoi-dap/question/56521.html?pos=147113

\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}+\frac{x+4}{2011}=0\)

\(\Leftrightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)+\left(\frac{x+4}{2011}+1\right)=0+1+1+1+1\)

\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}+\frac{x+2015}{2011}=4\)

\(\Leftrightarrow\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)=4\)

\(\Leftrightarrow x+2015=4:\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\right)\)

\(\Leftrightarrow x+2015=2012,499379\)

\(\Leftrightarrow x=2012,499379-2015\)

\(\Leftrightarrow x=-2,5006118\)

P/s : Số xấu quá !

a: Sửa đề: \(\dfrac{2x-1}{11}+\dfrac{2x-2}{12}+\dfrac{2x-3}{13}=\dfrac{2x+5}{5}+\dfrac{2x+7}{3}+\dfrac{2x+4}{6}\)

\(\Leftrightarrow\dfrac{2x-1}{11}+1+\dfrac{2x-2}{12}+1+\dfrac{2x-3}{13}+1=\dfrac{2x+5}{5}+1+\dfrac{2x+7}{3}+1+\dfrac{2x+4}{6}+1\)

=>2x+10=0

hay x=-5

b: \(\dfrac{x-1}{2016}+\dfrac{x-2}{2015}+\dfrac{x-3}{2014}+\dfrac{x-4}{2013}+\dfrac{x-5}{2012}-5=0\)

\(\Leftrightarrow\left(\dfrac{x-1}{2016}-1\right)+\left(\dfrac{x-2}{2015}-1\right)+\left(\dfrac{x-3}{2014}-1\right)+\left(\dfrac{x-4}{2013}-1\right)+\left(\dfrac{x-5}{2012}-1\right)=0\)

=>x-2017=0

hay x=2017