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\(\frac{x-2}{2016}+\frac{x-3}{2017}+\frac{x-4}{2018}+3=0\)
\(\Leftrightarrow\left(\frac{x-2}{2016}+1\right)+\left(\frac{x-3}{2017}+1\right)+\left(\frac{x-4}{2018}+1\right)=0\)
\(\Leftrightarrow\frac{x+2014}{2016}+\frac{x+2014}{2017}+\frac{x+2014}{2018}=0\)
\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)=0\)
Mà \(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\ne0\)
\(\Leftrightarrow x+2014=0\)
\(\Leftrightarrow x=-2014\)
Vậy \(x=-2014\)
\(\frac{x-1}{2018}+\frac{x-2}{2017}+\frac{x-3}{2016}+\frac{x-2043}{8}\)\(=0\)
\(\Leftrightarrow\)\(\frac{x-1}{2018}-1+\frac{x-2}{2017}-1+\frac{x-3}{2016}-1\)\(+\frac{x-2043}{8}+3=0\)
\(\Leftrightarrow\)\(\frac{x-1}{2018}-\frac{2018}{2018}+\frac{x-2}{2017}-\frac{2017}{2017}\)\(+\frac{x-3}{2016}-\frac{2016}{2016}+\frac{x-2043}{8}+\frac{24}{8}=0\)
\(\Leftrightarrow\)\(\frac{x-2019}{2018}+\frac{x-2019}{2017}+\frac{x-2019}{2016}\)\(+\frac{x-2019}{8}=0\)
\(\Leftrightarrow\)\(\left(x-2019\right).\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{8}\right)=0\)
\(\Leftrightarrow\)\(x-2019=0\) ( Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{8}\ne0\))
\(\Leftrightarrow\) \(x=2019\)
Vậy phương trình có nghiệm là : \(x=2019\)
\(\frac{x-2}{2016}+\frac{x-3}{2017}+\frac{x-4}{2018}+3=0\\ \Leftrightarrow\left(\frac{x-2}{2016}+1\right)+\left(\frac{x-3}{2017}+1\right)+\left(\frac{x-4}{2018}+1\right)=0\\ \Leftrightarrow\frac{x+2014}{2016}+\frac{x+2014}{2017}+\frac{x+2014}{2018}=0\\ \Leftrightarrow\left(x+2014\right)\left(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)=0\\ Vì\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\ne0\\ \Rightarrow x+2014=0\\ \Leftrightarrow x=-2014\\ Vậy...\)
Ta có\(\frac{x-2}{2016}+\frac{x-3}{2017}+\frac{x-4}{2018}+3=0\)
\(\Leftrightarrow\frac{x-2}{2016}+1+\frac{x-3}{2017}+1+\frac{x-4}{2018}=0\)
\(\Leftrightarrow\frac{x+2014}{2016}+\frac{x+2014}{2017}+\frac{x+2014}{2018}=0\)
\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)=0\) Vì \(\left(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)>0\)
\(\Rightarrow x+2014=0\)
\(\Rightarrow x=-2014\)