Question

Решите Неравенство

Answer 1

$\frac{(x-2)(2x-1)}{2x^2+7x+3}>0\\\\2x^2+7x+3=0\; ,\; \; D=25\; ,\; \; x_1=-3\; ,\; x_2=-\frac{1}{2}\\\\\frac{(x-2)(2x-1)}{2(x+3)(x-\frac{1}{2})}>0\; ,\; \; \frac{(x-2)(2x-1)}{(x+3)(2x-1)}>0\; \; \to \; \; ODZ:\; \; x\ne -3\; ,\; \; x\ne -\frac{1}{2}\\\\\frac{x-2}{x+3}>0\\\\znaki:\; \; \; +++(-3)---(-\frac{1}{2})---(2)+++\\\\x\in (-\infty ,-3)\cup (2,+\infty )$