Đáp án:
\(x = - 1010\)
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{x + 1}}{{1009}} + 1 - \dfrac{{2x + 3}}{{2017}} + 1 = \dfrac{{6x - 1}}{{6061}} + 1 - \dfrac{{3x - 1}}{{3031}} + 1\\
\to \dfrac{{x + 1010}}{{1009}} - \dfrac{{2x + 2020}}{{2017}} = \dfrac{{6x + 6060}}{{6061}} - \dfrac{{3x - 3030}}{{3031}}\\
\to \dfrac{{x + 1010}}{{1009}} - \dfrac{{2\left( {x + 1010} \right)}}{{2017}} = \dfrac{{6\left( {x + 1010} \right)}}{{6061}} - \dfrac{{3\left( {x + 1010} \right)}}{{3031}}\\
\to \left( {x + 1010} \right)\left( {\dfrac{1}{{1009}} - \dfrac{2}{{2017}} - \dfrac{6}{{6061}} + \dfrac{3}{{3031}}} \right) = 0\\
\to x + 1010 = 0\\
\to x = - 1010
\end{array}\)
