12.x-33=3^2014/3^2013
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\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{3x+12}{2011}\)
\(\Leftrightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)=\frac{3x+12}{2011}+3\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=\frac{3x+6045}{2011}\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}-\frac{3\left(x+2015\right)}{2011}=0\)
\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{3}{2011}\right)=0\)
Mà \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{3}{2011}\ne0\)
\(\Leftrightarrow x+2015=0\)
\(\Leftrightarrow x=-2015\)
Vậy x = -2015
\(x-2014-\frac{2015}{2013}+x-2013-\frac{2015}{2014}+x-2014-\frac{2013}{2015}=3\)
\(\Rightarrow\left(x+x+x\right)+\left(-2014-2014\right)-2013-\frac{2015}{2013}-\frac{2015}{2014}-\frac{2013}{2015}=3\)
\(3x-2013-\frac{2015}{2013}-\frac{2015}{2014}-\frac{2013}{2015}=3\)
\(3x=3+2013+\frac{2015}{2013}+\frac{2015}{2014}+\frac{2013}{2015}\)
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\(\dfrac{x-3}{2013}+\dfrac{x-2}{2014}=\dfrac{x-2014}{2}+\dfrac{x-2013}{3}\)
\(\Leftrightarrow\dfrac{x-3}{2013}-1+\dfrac{x-2}{2014}-1=\dfrac{x-2014}{2}-1+\dfrac{x-2013}{3}-1\)
\(\Leftrightarrow\dfrac{x-3-2013}{2013}+\dfrac{x-2-2014}{2014}=\dfrac{x-2014-2}{2}+\dfrac{x-2013-3}{3}\)
\(\Leftrightarrow\dfrac{x-2016}{2013}+\dfrac{x-2016}{2014}=\dfrac{x-2016}{2}+\dfrac{x-2016}{3}\)
\(\Leftrightarrow\dfrac{x-2016}{2013}+\dfrac{x-2016}{2014}-\dfrac{x-2016}{2}-\dfrac{x-2016}{3}=0\)
\(\Leftrightarrow\left(x-2016\right)\left(\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2}-\dfrac{1}{3}\right)=0\)
Vì \(\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2}-\dfrac{1}{3}\ne0\)
\(\Rightarrow x-2016=0\)
\(\Leftrightarrow x=2016\)( thỏa mãn )
Vậy x = 2016
\(\dfrac{x-3}{2013}+\dfrac{x-2}{2014}=\dfrac{x-2014}{2}+\dfrac{x-2013}{3}\)
\(\Leftrightarrow\dfrac{x-3}{2013}-1+\dfrac{x-2}{2014}-1=\dfrac{x-2014}{2}-1+\dfrac{x-2013}{3}-1\)
\(\Leftrightarrow\dfrac{x-2016}{2013}+\dfrac{x-2016}{2014}=\dfrac{x-2016}{2}+\dfrac{x-2016}{3}\)
\(\Leftrightarrow\left(x-2016\right)\left(\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2}-\dfrac{1}{3}\right)=0\)
\(\Leftrightarrow x-2016=0\) (do \(\dfrac{1}{2013}+\dfrac{1}{2014}-\dfrac{1}{2}-\dfrac{1}{3}\ne0\))
\(\Rightarrow x=2016\)