[tex]\displaystyle\bf\\\frac{x-5}{x+5} < x\\\\\\\frac{x-5}{x+5}-x < 0\\\\\\\frac{x-5-x\cdot(x+5)}{x+5} < 0\\\\\\\frac{x-5-x^{2} -5x}{x+5} < 0\\\\\\\frac{-x^{2} -4x-5}{x+5} < 0\\\\\\\frac{x^{2} +4x+5}{x+5} > 0\\\\\\x^{2} +4x+5 > 0 \ \ pri \ \ x\in R \ \ \Rightarrow \ \ \ x+5 > 0 \ \ \ \Rightarrow \ \ x > -5\\\\\\Otvet \ \ : \ \ x\in\Big(-5 \ ; \ +\infty\Big)[/tex]
Наименьшее целое решение неравенства : -4
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[tex]\displaystyle\bf\\\frac{x-5}{x+5} < x\\\\\\\frac{x-5}{x+5}-x < 0\\\\\\\frac{x-5-x\cdot(x+5)}{x+5} < 0\\\\\\\frac{x-5-x^{2} -5x}{x+5} < 0\\\\\\\frac{-x^{2} -4x-5}{x+5} < 0\\\\\\\frac{x^{2} +4x+5}{x+5} > 0\\\\\\x^{2} +4x+5 > 0 \ \ pri \ \ x\in R \ \ \Rightarrow \ \ \ x+5 > 0 \ \ \ \Rightarrow \ \ x > -5\\\\\\Otvet \ \ : \ \ x\in\Big(-5 \ ; \ +\infty\Big)[/tex]
Наименьшее целое решение неравенства : -4