\(x+\dfrac{5}{2017}+x+\dfrac{6}{2018}+x+\dfrac{7}{2019}=-3\)
\(\Leftrightarrow3x+\dfrac{5}{2017}+\dfrac{6}{2018}+\dfrac{7}{2019}=-3\)
\(\Leftrightarrow\dfrac{5}{2017}+\dfrac{6}{2018}+\dfrac{7}{2019}=-3-3x\)
\(\Leftrightarrow\dfrac{5}{2017}+\dfrac{6}{2018}+\dfrac{7}{2019}=-3\left(x+1\right)\)
\(\Leftrightarrow\dfrac{5}{6051}+\dfrac{6}{6054}+\dfrac{7}{6057}=-x-1\)
\(\Leftrightarrow-x=\dfrac{5}{6051}+\dfrac{1}{3}+\dfrac{6}{6054}+\dfrac{1}{3}+\dfrac{7}{6057}+\dfrac{1}{3}\)
\(\Leftrightarrow-x=\dfrac{674}{2017}+\dfrac{1012}{3027}+\dfrac{2026}{6057}\)
\(\Leftrightarrow x=-\dfrac{674}{2017}-\dfrac{1012}{3027}-\dfrac{2026}{6057}\)