[tex]x+ \frac{4 x^{2} +5x}{ x^{2} -x-6} \leq \frac{9}{5x-15}+ \frac{5x+1}{5x+10} [/tex]. Created by Swetta2013. algebra-ru

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

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

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