\(\frac{x-1}{2018}+\frac{x-10}{2009}+\frac{x-19}{2000}=3\)
\(\frac{x-1}{2018}+\frac{x-10}{2009}+\frac{x-19}{2000}-3=0\)
\(\left(\frac{x-1}{2018}-1\right)+\left(\frac{x-10}{2009}-1\right)+\left(\frac{x-19}{2000}-1\right)=0\)
\(\frac{x-1-2018}{2018}+\frac{x-10-2009}{2009}+\frac{x-19-2000}{2000}=0\)
\(\frac{x-2019}{2018}+\frac{x-2019}{2009}+\frac{x-2019}{2000}=0\)
\(\left(x-2019\right)\left(\frac{1}{2018}+\frac{1}{2009}+\frac{1}{2000}\right)=0\)
Vì \(\left(\frac{1}{2018}+\frac{1}{2009}+\frac{1}{2000}\right)\ne0\)do đó :
\(x-2019=0\)
\(x=2019\)
\(\frac{x-1}{2018}+\frac{x-10}{2009}+\frac{x-19}{2000}=3.\)
\(\Leftrightarrow\frac{x-1}{2018}-1+\frac{x-10}{2009}-1+\frac{x-19}{2000}-1=0\)
\(\Leftrightarrow\frac{x-2019}{2018}+\frac{x-2019}{2009}+\frac{x-2019}{2000}=0\)
\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{2018}+\frac{1}{2009}+\frac{1}{2000}\right)=0\)
\(\Leftrightarrow x-2019=0\Leftrightarrow x=2019\)
\(\frac{x-1}{2018}+\frac{x-10}{2009}+\frac{x-19}{2000}=3\)
\(\Rightarrow\left(\frac{x-1}{2018}-1\right)+\left(\frac{x-10}{2009}-1\right)+\left(\frac{x-19}{2000}-1\right)=0\)
\(\Rightarrow\frac{x-2019}{2018}+\frac{x-2019}{2009}+\frac{x-2019}{2000}=0\)
\(\Rightarrow\left(x-2019\right)\left(\frac{1}{2018}+\frac{1}{2009}+\frac{1}{2000}\right)=0\)
\(\Rightarrow x-2019=0\left(Vì\frac{1}{2018}+\frac{1}{2009}+\frac{1}{2000}\ne0\right)\)
\(\Rightarrow x=2019\)
