Question

Решите неравенство
1)$frac{x+16}{x-11} textless 0$
2$frac{x-8}{x+4} textgreater 0$

Answer 1

$1) left { {{x+16 textgreater 0} atop {x-11 textless 0}} right. Longleftrightarrow left { {{x textgreater -16} atop {x textless 11}} right. Rightarrow xin (-16;11)$
$left { {{x+16 textless 0} atop {x-11 textgreater 0}} right. Longleftrightarrow left { {{x textless -16} atop {x textgreater 11}} right. Rightarrow$ решений нет.
Ответ: $xin (-16;11)$
$2) left { {{x-8 textgreater 0} atop {x+4 textgreater 0}} right. Longleftrightarrow left { {{x textgreater 8} atop {x textgreater -4}} right. Rightarrow x in (8;+infty)$
$left { {{x-8 textless 0} atop {x+4 textless 0}} right. Longleftrightarrow left { {{x textless 8} atop {x textless -4}} right. Rightarrow xin (-infty;-4)$
Ответ: $xin (-infty;-4)cup(8; +infty)$