Question

$x+ frac{4 x^{2} +5x}{ x^{2} -x-6} leq frac{9}{5x-15}+ frac{5x+1}{5x+10}$

Answer 1

$x+frac{4x^2+5x}{x^2-x-6} leq frac{9}{5(x-3)}+frac{5x+1}{5(x+2)}\\ frac{x^3-x^2-6x+4x^2+5x}{x^2-x-6} leq frac{9(x+2) +(x-3)(5x+1)}{5(x^2-x-6)}\\ 5(x^3-x^2-6x+4x^2+5x) leq 5x^2-5x+15\\ x neq 3\\ x neq -2 \\ x^3+3x^2-x leq x^2-x+3 \\ x^3+2x^2-3 leq 0 \\ (x-1)(x^2+3x+3) leq 0\\ x leq 1\\ x^2+3x+3 geq 0\ D<0$ 
Ответ    $xin(infty;-2)cup[1;3)$