Question

Giải phương trình: \(\dfrac{x+2}{2011}\)+\(\dfrac{x+2017}{4}\)=\(\dfrac{x+4}{2009}\)+\(\dfrac{x+2019}{6}\)

Answer 1

\(\dfrac{x+2}{2011}+\dfrac{x+2017}{4}=\dfrac{x+4}{2009}+\dfrac{x+2019}{6}\)

\(\Leftrightarrow\dfrac{x+2013-2011}{2011}+\dfrac{x+2013+4}{4}=\dfrac{x+2013-2009}{2009}+\dfrac{x+2013+6}{6}\)

\(\Leftrightarrow\dfrac{x+2013}{2011}-1+\dfrac{x+2013}{4}+1=\dfrac{x+2013}{2009}-1+\dfrac{x+2013}{6}+1\)

\(\Leftrightarrow\dfrac{x+2013}{2011}+\dfrac{x+2013}{4}-\dfrac{x+2013}{2009}-\dfrac{x+2013}{6}=0\)

\(\Leftrightarrow\left(x+2013\right)\left(\dfrac{1}{2011}+\dfrac{1}{4}-\dfrac{1}{2009}-\dfrac{1}{6}\right)=0\)

\(\Leftrightarrow x+2013=0\)

\(\Leftrightarrow x=-2013\)

Vậy PT trên có nghiệm là S={-2013}