Решите неравенство 2x+1- 21x+39/x^2+x-2>=-1/x+2. Created by 0993772391. algebra-ru

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Решите неравенство 2x+1- 21x+39/x^2+x-2>=-1/x+2

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$2x+1- \dfrac{21x+39}{x^2+x-2} \geq \dfrac{-1}{x+2}\\\\\\2x+1- \dfrac{21x+39}{(x+2)(x-1)}+ \dfrac{1}{x+2}\geq 0\; ,\; \; \ \ ODZ:\ x\ne -2\; ,\; x\ne 1\\\\\\\dfrac{(2x+1)(x+2)(x-1)-21x-39+x-1}{(x+2)(x-1)}\geq 0\\\\\\\dfrac{2x^3+3x^2-23x-42}{(x+2)(x-1)}\geq 0\\\\\\ \dfrac{(x+2)(x+3)(x-3,5)}{(x+2)(x-1)}\geq 0\\\\\\\dfrac{(x+3)(x-3,5)}{x-1}\geq 0\\\\\\znaki:\ \ ---[-3\ ]+++(-2)+++(1)---[\ 3,5\ ]+++\\\\\\x\in [\, -3,-2)\cup (-2,1)\cup [\ 3,5\ ;+\infty \, )$

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