[tex]\frac{2x+2}{2018}-\frac{2x+3}{2017}=\frac{6x-1}{6061}-\frac{6x-2}{6062}[/tex]
[tex]\Leftrightarrow \frac{2x+2020}{2018}-\frac{2x+2020}{2017}=\frac{6x+6060}{6061}-\frac{6x+6060}{6062}[/tex]
[tex]\Leftrightarrow 2(x+1010)(\frac{1}{2018}-\frac{1}{2017})=2(x+1010)(\frac{3}{6061}-\frac{3}{6062})[/tex]
[tex]\Leftrightarrow 2(x+1010)(\frac{1}{2018}-\frac{1}{2017}-\frac{3}{6061}+\frac{3}{6062}=0)[/tex]
Do [tex] 2(\frac{1}{2018}-\frac{1}{2017}-\frac{3}{6061}+\frac{3}{6062})\neq 0[/tex]
[tex] \Rightarrow (x+1010)=0 \Rightarrow x=-1010 [/tex]