Question

Решите методом интервалов неравенство 4-x/x-2>1

Answer 1

$\frac{4-x}{x-2}\ \textgreater \ 1\\\\ \frac{-(x-4)}{x-2}\ \textgreater \ 1\\\\ \frac{x-4}{x-2}\ \textless \ -1\\\\ \frac{x-4}{x-2}+1\ \textless \ 0\\\\ \frac{x-4}{x-2}+\frac{x-2}{x-2}\ \textless \ 0\\\\ \frac{x-4+x-2}{x-2}\ \textless \ 0\\\\ \frac{2x-6}{x-2}\ \textless \ 0\\\\ \frac{2(x-3)}{x-2}\ \textless \ 0\\\\ \frac{x-3}{x-2}\ \textless \ 0\\\\ +++++++(2)--------(3)++++++\ \textgreater \ x\\\\ x\in(2;\ 3)$