Đáp án:
a) x=13
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{x - 1}}{{12}} - 1 + \dfrac{{x - 6}}{7} - 1 = \dfrac{{x + 12}}{{25}} - 1 + \dfrac{{x + 14}}{{27}} - 1\\
\to \dfrac{{x - 13}}{{12}} + \dfrac{{x - 13}}{7} = \dfrac{{x - 13}}{{25}} + \dfrac{{x - 13}}{{27}}\\
\to \left( {x - 13} \right)\left( {\dfrac{1}{{12}} + \dfrac{1}{7} - \dfrac{1}{{25}} - \dfrac{1}{{27}}} \right) = 0\\
\to x - 13 = 0\\
\to x = 13\\
b)\dfrac{{x + 1}}{{99}} + 1 + \dfrac{{x + 2}}{{98}} + 1 + \dfrac{{x + 3}}{{97}} + 1 + ... + \dfrac{{x + 50}}{{50}} + 1 = 0\\
\to \dfrac{{x + 100}}{{99}} + \dfrac{{x + 100}}{{98}} + \dfrac{{x + 100}}{{97}} + ... + \dfrac{{x + 100}}{{50}} = 0\\
\to \left( {x + 100} \right)\left( {\dfrac{1}{{99}} + \dfrac{1}{{98}} + \dfrac{1}{{97}} + ... + \dfrac{1}{{50}}} \right) = 0\\
\to x + 100 = 0\\
\to x = - 100
\end{array}\)
