Question

Решите неравенства.
Номера 577 (1,2) и 578 (1).

Answer 1

577 (1)
$\frac{x+2}{3-x}\ \textgreater \ 0\\\\ \frac{x+2}{-(x-3)}\ \textgreater \ 0\\\\ -\frac{x+2}{x-3}\ \textgreater \ 0\\\\ \frac{x-(-2)}{x-3}\ \textless \ 0\\\\ ++++++++(-2)-----------(3)++++++\ \textgreater \ x\\\\ x\in(-2;\ 3)$

577 (2)
$\frac{x-10}{2-x}\ \textless \ 0\\\\ -\frac{x-10}{x-2}\ \textless \ 0\\\\ \frac{x-10}{x-2}\ \textgreater \ 0\\\\ +++++++++(2)-------(10)+++++++++\ \textgreater \ x\\\\ x\in(-\infty;\ 2)\cup(10;\ +\infty)$

578 (1)
$\frac{x^2-6x}{x^2-6x+9} \leq 0\\\\ \frac{x(x-6)}{(x-3)^2} \leq 0\\\\ \frac{(x-0)*(x-6)}{(x-3)^2} \leq 0\\\\ ++++++[0]------(3)------[6]++++++\ \textgreater \ x\\\\ x\in[0;\ 3)\cup(3;\ 6]$