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

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

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

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

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

\(\Rightarrow\hept{\begin{cases}x+2015=0\\\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}=0\end{cases}}\)

Vì \(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\ne0\Rightarrow x+2015=0\Rightarrow x=-2015\)

Vậy x = 2015 nha bn

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

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

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

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

\(\Rightarrow\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\right)\)

Vì \(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\ne0\Rightarrow\left(x-2015\right)=0\)

\(\Rightarrow x=0+2015\) =2015

Đúng thì k ủng hộ mik nha mn!

a) \(\frac{x+4}{2009}+1+\frac{x+3}{2010}+1=\frac{x+2}{2011}+1+\frac{x+1}{2012}\)

\(\frac{x+4+2009}{2009}+\frac{x+3+2010}{2010}=\frac{x+2+2011}{2011}+\frac{x+2+2012}{2012}\)

\(\frac{x+2013}{2009}+\frac{x+2013}{2010}-\frac{x+2013}{2011}-\frac{x+2013}{2012}=0\)

\(\left(x+2013\right).\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=0\)    (1)

Vì \(\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)\ne0\)

Nên biểu thức (1) xảy ra khi \(x+2013=0\)

\(x=-2013\)

b) \(\left(x-2011\right)\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\)  (2)

Vì \(\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)\ne0\)

Nên biểu thức (2) xảy ra khi \(x-2011=0\)

\(x=2011\)

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

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

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

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

\(\Leftrightarrow x+2015=0\) (Vì: \(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\ne0\) )

\(\Leftrightarrow x=-2015\)

bấm vào chữ xanh này nha bn : /hoi-dap/question/113985.html

trước tiên bạn phải tính:

2013/1+2012/2+2011/3+.....+2/2012+1/2013

=1+2012/2)+(1+2011/3)+.....+(1+2/2012)+(1+1/2013) +1 {BƯỚC NÀY TÁCH 2013 RA LÀM 2013SỐ1 ĐỂ CÔNG VS CÁC THỪA SỐ CÒN LẠI}

=2014/2+2014/3+...+2014/2012+2014/2013+2014/2014

=2014.(1/2+1/3+....+1/2012+1/20131/2014

suy ra x=2014

cong 1 vao tung hang tu (vd 3/2013) roi dc tong 2016