Вопрос:

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

Ответ:

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

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

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

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

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

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

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

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

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

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