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 \(x=-2015\).

Câu 1 bị sai đề bài.

Câu 2:

\(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}=\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}\)

\(=1-\frac{1}{2012}+1-\frac{1}{2013}+1+\frac{1}{2011}+\frac{1}{2011}\)

Vì:

\(\frac{1}{2011}>\frac{1}{2012};\frac{1}{2011}>\frac{1}{2013}\Rightarrow\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2012}-\frac{1}{2013}>0\)

\(\Rightarrow\)\(\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}>3\)

\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}>3\)

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bài này khó lắm đó

\(\text{Đầu bài viết khó nhìn thí mồ!! viết lại nhé!!}\)

\(\frac{x+1}{2013}+\frac{x+2}{2012}+\frac{x+3}{2011}=\frac{x-1}{2015}+\frac{x-2}{2016}+\frac{x-3}{2017}\)

\(\Rightarrow\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=\frac{x-1}{2015}+1+\frac{x-2}{2016}+1+\frac{x-3}{2017}+1\)

\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}-\frac{x+2014}{2015}-\frac{x+2014}{2016}-\frac{x+2014}{2017}=0\)

\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)

\(\text{Mà }\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\)

\(\text{Nên }x+2014=0\Leftrightarrow x=-2014\)

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

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

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

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

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

=>x+2014=0 (vì \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}\) khác 0)

=>x=-2014

x = -1 vì nếu x nguyên dương ta sẽ không có được x bởi 2013 = 2013 rồi

Theo đề bài ta có, x + ( x +1 ) nên  chỉ có khả năng x là x là số âm thôi vì nếu x là số âm thì mới cộng với 2012 +2013 = 2013 được. Vậy theo mình nghĩ số nguyên âm mà phù hợp x là -1.

nếu đúng thì xin bạn hãy mình nhé

Anh tôi mới làm bài này hôm qua xong:

x+(x+1)+(x+2)+ ... + 2012+2013 = 2013

Suy ra: x+(x+1)+(x+2)+...+2012= 2013-2013 = 0

= [x+2012] + [(x+1)+ 2011] +... = 0

= (x+2012)(1+1+...+1) = 0

Bởi (1+1+...+1) khác 0 nên:

x + 2012 = 0 suy ra: x = 0 - 2012 = -2012.

Vậy : x = -2012.

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

=> \(\frac{x+5}{2011}+\frac{x+2015}{2012}=\frac{x+2015}{2013}+\frac{x+2015}{2014}\)

=> \(\left(x+2015\right)\left(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\)

=> x = -2015 Vì \(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\ne0\)