Đáp án:
c) x=100
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{x - 23}}{{24}} + \dfrac{{x - 23}}{{25}} = \dfrac{{x - 23}}{{26}} + \dfrac{{x - 23}}{{27}}\\
\to \left( {x - 23} \right)\left( {\dfrac{1}{{24}} + \dfrac{1}{{25}} - \dfrac{1}{{26}} - \dfrac{1}{{27}}} \right) = 0\\
\to x - 23 = 0\\
\to x = 23\\
b)\dfrac{{x + 2}}{{98}} + \dfrac{{x + 3}}{{97}} = \dfrac{{x + 4}}{{96}} + \dfrac{{x + 5}}{{95}}\\
\to \dfrac{{x + 2}}{{98}} + 1 + \dfrac{{x + 3}}{{97}} + 1 = \dfrac{{x + 4}}{{96}} + 1 + \dfrac{{x + 5}}{{95}} + 1\\
\to \dfrac{{x + 100}}{{98}} + \dfrac{{x + 100}}{{97}} = \dfrac{{x + 100}}{{96}} + \dfrac{{x + 100}}{{95}}\\
\to \left( {x + 100} \right)\left( {\dfrac{1}{{98}} + \dfrac{1}{{97}} - \dfrac{1}{{96}} - \dfrac{1}{{95}}} \right) = 0\\
\to x = - 100\\
c)\dfrac{{x - 45}}{{55}} + \dfrac{{x - 47}}{{53}} = \dfrac{{x - 51}}{{49}} + \dfrac{{x - 53}}{{47}}\\
\to \dfrac{{x - 45}}{{55}} - 1 + \dfrac{{x - 47}}{{53}} - 1 = \dfrac{{x - 51}}{{49}} - 1 + \dfrac{{x - 53}}{{47}} - 1\\
\to \dfrac{{x - 100}}{{55}} + \dfrac{{x - 100}}{{53}} - \dfrac{{x - 100}}{{49}} - \dfrac{{x - 100}}{{47}} = 0\\
\to \left( {x - 100} \right)\left( {\dfrac{1}{{55}} + \dfrac{1}{{53}} - \dfrac{1}{{49}} - \dfrac{1}{{47}}} \right) = 0\\
\to x - 100 = 0\\
\to x = 100
\end{array}\)
