Question

giải phương trình x-2/2016 +x-4/1009+x-6/2020=-4

Answer 1

\(\dfrac{x-2}{2016}+\dfrac{x-4}{1009}+\dfrac{x-6}{2020}=-4\)

\(\Leftrightarrow\) \(\dfrac{x-2}{2016}+1+\dfrac{x-4}{1009}+2+\dfrac{x-6}{2020}+1=0\)

\(\Leftrightarrow\) \(\dfrac{x-2+2016}{2016}+\dfrac{x-4+2018}{1009}+\dfrac{x-6+2020}{2020}=0\)

\(\Leftrightarrow\) \(\dfrac{x-2014}{2016}+\dfrac{x-2014}{1009}+\dfrac{x-2014}{2020}=0\)

\(\Leftrightarrow\) \(\left(x-2014\right)\left(\dfrac{1}{2016}+\dfrac{1}{1009}+\dfrac{1}{2020}\right)=0\)

\(\Leftrightarrow\) x - 2014 = 0

\(\Leftrightarrow\) x = 2014

Vậy............