Вопрос:

Решите неравенство: (x^2-2x-15)/(x^2-2x-3)>=0.

Ответ:

\[\frac{x^{2} - 2x - 15}{x^{2} - 2x - 3} \geq 0\]

\[x^{2} - 2x - 15 =\]

\[= x^{2} - 5x + 3x - 15 =\]

\[= x(x - 5) + 3(x - 5) =\]

\[= (x - 5)(x + 3)\]

\[x^{2} - 2x - 3 = x^{2} - 3x + x - 3 =\]

\[= x(x - 3) + (x - 3) =\]

\[= (x - 3)(x + 1)\]

\[\frac{(x + 3)(x - 5)}{(x + 1)(x - 3)} \geq 0\]

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