1. (1/x-1) + 2/x amp;gt; (1/x+1)2. (x+1)(x+2)(x+3)/(x-1)(x-2)(x-3)amp;gt;1

$1)\; \; \frac1x-1+\frac2xgt;\frac1x+1\\\\\fracx(x+1)+2(x-1)(x+1)-x(x-1)x(x-1)(x+1)gt;0\\\\\fracx^2+x+2x^2-2-x^2+xx(x-1)(x+1)gt;0\\\\\frac2(x^2+x-1)x(x-1)(x+1) gt;0\\\\x^2+x-1=0\; ,\; \; D=1+4=5\; ,\; x_1,2=\frac-1\pm \sqrt52\\\\x_1\approx -1,62\; ,\; \; x_2\approx 0,62\\\\---( -1,62)+++(-1)---(0)+++(0,62)---(1)+++\\\\x\in (\frac-1-\sqrt52,-1)\cup (0,\frac-1+\sqrt52)\cup (1,+\infty )$

$2)\; \; \frac(x+1)(x+2)(x+3)(x-1)(x-2)(x-3)gt;1\\\\\frac(x+1)(x+2)(x+3)-(x-1)(x-2)(x-3)(x-1)(x-2)(x-3)gt;0\\\\\frac(x^2+3x+2)(x+3)-(x^2-3x+2)(x-3)(x-1)(x-2)(x-3)gt;0\\\\\fracx^3+3x^2+3x^2+9x+2x+6-(x^3-3x^2-3x^2+9x+2x-6)(x-1)(x-2)(x-3)gt;0\\\\\frac12x^2+12(x-1)(x-2)(x-3)gt;0\; ,\; \; \frac12(x^2+1)(x-1)(x-2)(x-3)gt;0\\\\12(x^2+1)gt;0\; \; pri\; \; x\in (-\infty ,+\infty )\; \; \Rightarrow (x-1)(x-2)(x-3)gt;0\\\\---(1)+++(2)---(3)+++\\\\x\in (1,2)\cup (3,+\infty )$

О проекте

1. (1/x-1) + 2/x amp;gt; (1/x+1)2. (x+1)(x+2)(x+3)/(x-1)(x-2)(x-3)amp;gt;1

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