[latex]x+ \frac{4 x^{2} +5x}{ x^{2} -x-6} \leq \frac{9}{5x-15}+ \frac{5x+1}{5x+10} [/latex]

[latex]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\\\\ [/latex]  Ответ    [latex] x\in(\infty;-2)\cup[1;3) [/latex]