Giai phương trình sau : x+1 / 15 + x +2 /14 = x+3 /13 + x+4/ 12
Giải thích
Ta có: \(\frac{{x + 1}}{{15}} + \frac{{x + 2}}{{14}} = \frac{{x + 3}}{{13}} + \frac{{x + 4}}{{12}}\)
\(\frac{{x + 1}}{{15}} + 1 + \frac{{x + 2}}{{14}} + 1 = \frac{{x + 3}}{{13}} + 1 + \frac{{x + 4}}{{12}} + 1\)
\(\frac{{x + 16}}{{15}} + \frac{{x + 16}}{{14}} = \frac{{x + 16}}{{13}} + \frac{{x + 16}}{{12}}\)
\(\frac{{x + 16}}{{15}} + \frac{{x + 16}}{{14}} - \frac{{x + 16}}{{13}} - \frac{{x + 16}}{{12}} = 0\)
\(\left( {x + 16} \right)\left( {\frac{1}{{15}} + \frac{1}{{14}} - \frac{1}{{13}} - \frac{1}{{12}}} \right) = 0\)
Nhận thấy \(\left( {\frac{1}{{15}} + \frac{1}{{14}} - \frac{1}{{13}} - \frac{1}{{12}}} \right) \ne 0\) nên \(x + 16 = 0\) suy ra \(x = - 16.\)
Vậy \(x = - 16.\)