Question

Решить методом интервалов неравенство
$\frac{ {x}^{2} - 2x - 15}{ {x}^{2} + 6x} \leqslant 0$
​

Answer 1

x≠-6, x≠0

$\frac{ {x}^{2} - 2x - 15}{ {x}^{2} + 6x} \leqslant 0\\\\({x}^{2} - 2x - 15)(x^{2} + 6x) \leqslant 0\\\\(x-5x+3x-15)x(x+6)\leq 0\\\\\left[x(x-5)-3(x-5)\right] ]x(x+6)\leq 0\\\\x(x-5)(x-3)(x+6)\leq 0\\\\x\in(0;5]\cup(-6;-3]$