Tìm x
\(\frac{x-7}{2005}+\frac{x-6}{2006}=\frac{x-5}{2007}+\frac{x-4}{2008}\)
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\(\frac{x-7}{2005}+\frac{x-6}{2006}=\frac{x-5}{2007}+\frac{x-4}{2008}\)
\(\Rightarrow\frac{x-7}{2005}-1+\frac{x-6}{2006}-1=\frac{x-5}{2007}-1+\frac{x-4}{2008}-1\)
\(\Rightarrow\frac{x-2012}{2005}+\frac{x-2012}{2006}=\frac{x-2012}{2007}+\frac{x-2012}{2008}\)
\(\Rightarrow\frac{x-2012}{2005}+\frac{x-2012}{2006}-\frac{x-2012}{2007}-\frac{x-2012}{2008}=0\)
\(\Rightarrow\left(x-2012\right)\left(\frac{1}{2005}+\frac{1}{2006}-\frac{1}{2007}-\frac{1}{2008}\right)=0\)
\(\Rightarrow x-2012=0\). Do \(\frac{1}{2005}+\frac{1}{2006}-\frac{1}{2007}-\frac{1}{2008}\ne0\)
\(\Rightarrow x=2012\)
\(\frac{x-7}{2005}+\frac{x-6}{2006}=\frac{x-5}{2007}+\frac{x-4}{2008}\)
\(\Rightarrow\left(\frac{x-7}{2005}-1\right)+\left(\frac{x-6}{2006}-1\right)=\left(\frac{x-5}{2007}-1\right)+\left(\frac{x-4}{2008}-1\right)\)
\(\Rightarrow\frac{x-2012}{2005}+\frac{x-2012}{2006}=\frac{x-2012}{2007}+\frac{x-2012}{2008}\)
\(\Rightarrow\frac{x-2012}{2005}+\frac{x-2012}{2006}-\frac{x-2012}{2007}-\frac{x-2012}{2008}=0\)
\(\Rightarrow\left(x-2012\right)\left(\frac{1}{2005}+\frac{1}{2006}-\frac{1}{2007}-\frac{1}{2008}\right)=0\)
Mà \(\left(\frac{1}{2005}+\frac{1}{2006}-\frac{1}{2007}-\frac{1}{2008}\right)\ne0\)
\(\Rightarrow x-2012=0\)
\(\Rightarrow x=2012\)
Vậy \(x=2012\)