Đáp án:
\[x = 9\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{x - 1}}{{12}} + \dfrac{{x - 1}}{{20}} + \dfrac{{x - 1}}{{30}} + \dfrac{{x - 1}}{{42}} + \dfrac{{x - 1}}{{56}} + \dfrac{{x - 1}}{{72}} = \dfrac{{16}}{9}\\
\Leftrightarrow \left( {x - 1} \right).\left( {\dfrac{1}{{12}} + \dfrac{1}{{20}} + \dfrac{1}{{30}} + \dfrac{1}{{42}} + \dfrac{1}{{56}} + \dfrac{1}{{72}}} \right) = \dfrac{{16}}{9}\\
\Leftrightarrow \left( {x - 1} \right).\left( {\dfrac{1}{{3.4}} + \dfrac{1}{{4.5}} + \dfrac{1}{{5.6}} + \dfrac{1}{{6.7}} + \dfrac{1}{{7.8}} + \dfrac{1}{{8.9}}} \right) = \dfrac{{16}}{9}\\
\Leftrightarrow \left( {x - 1} \right).\left( {\dfrac{1}{3} - \dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{6} + \dfrac{1}{6} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{8} + \dfrac{1}{8} - \dfrac{1}{9}} \right) = \dfrac{{16}}{9}\\
\Leftrightarrow \left( {x - 1} \right).\left( {\dfrac{1}{3} - \dfrac{1}{9}} \right) = \dfrac{{16}}{9}\\
\Leftrightarrow \left( {x - 1} \right).\dfrac{2}{9} = \dfrac{{16}}{9}\\
\Leftrightarrow x - 1 = 8\\
\Leftrightarrow x = 9
\end{array}\)
Vậy \(x = 9\)
