\(2012.\left|x-2011\right|+\left(x-2011\right)^2=2013\left|2011-x\right|\)

\(2012.\left|x-2011\right|+\left|x-2011\right|^2=2013\left|x-2011\right|\)

\(\left|x-2011\right|\left(2012+\left|x-2011\right|\right)=2013\left|x-2011\right|\)

\(\Rightarrow2012+\left|x-2011\right|=2013\)

\(\left|x-2011\right|=1\)

\(\Rightarrow\orbr{\begin{cases}x=2012\\x=-2010\end{cases}}\)

\(\frac{2011.2013-2011.2012}{2012.2011+2011.2013}\)

\(=\frac{2011.\left(2013-2012\right)}{2011.\left(2012+2013\right)}\)

\(=\frac{2011.1}{2011.4025}\)

\(=\frac{1}{4025}\)

bài này là bài Tính nha mọi người giải rõ ra giúp mik nha

\(\frac{2011x2013-2012x2011}{2012x2011+2011x2013}\)

\(=\frac{2011x\left(2013-2012\right)}{2011x\left(2012+2013\right)}\)

\(=\frac{2011x1}{2011x4025}\)

\(=\frac{1}{4025}\)

Ta có: \(\frac{x+4}{2010}+\frac{x+3}{2011}=\frac{x+2}{2012}+\frac{x+1}{2013}\) 

\(\Rightarrow\left(\frac{x+4}{2010}+1\right)+\left(\frac{x+3}{2011}+1\right)=\left(\frac{x+2}{2012}+1\right)+\left(\frac{x+1}{2013}+1\right)\)

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

\(\Rightarrow x=-2014\)

=>2012|x-2011|-|x-2011|+(x-2011)^2+2013>0

=>2011|x-2011|+(x-2011)^2+2013>0(luôn đúng)