Question

Помогите решить неравенство.

Answer 1

$\frac{3x+7}{x-2} \ \textgreater \ \frac{x-4}{2-x} \\ \\ \frac{3x+7}{x-2} - \frac{x-4}{2-x} \ \textgreater \ 0 \\ \\ \frac{(3x+7)(2-x)-(x-4)(x-2)}{(x-2)(2-x)} \ \textgreater \ 0 \\ \\ \frac{6x-3x^2+14-7x-x^2+2x+4x-8}{(x-2)(2-x)} \ \textgreater \ 0 \\ \\ \frac{-4x^2+5x+6}{(x-2)(2-x)} \ \textgreater \ 0 \\ \\ -4x^2+5x+6=0 \\ D=25-4*(-4)*6=25+96=121 \\ \\ x_1= \frac{-5+11}{-8} = \frac{6}{-8} =- \frac{3}{4} =-0,75 ~~~~~~~~~~~~~~~~ x_2= \frac{-5-11}{-8} = \frac{-16}{-8} =2$

______+_____$-0,75$_____-______$2$______+______

Ответ: $x\in(-\infty;-0,75)\textup{ U }(2;+\infty)$