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МатематикаВопрос:
б) \(\frac{r^2 - 25}{r+3}\)\(\cdot\) \(\frac{1}{r^2+5r}\)-\(\frac{r+5}{r^2-3r}\);
Ответ:
Преобразуем выражение:
- $$\frac{r^2 - 25}{r+3} = \frac{(r-5)(r+5)}{r+3}$$
- $$\frac{1}{r^2+5r} = \frac{1}{r(r+5)}$$
- $$\frac{r+5}{r^2-3r} = \frac{r+5}{r(r-3)}$$
Выполним умножение первой дроби на вторую:
$$\frac{(r-5)(r+5)}{r+3}\cdot \frac{1}{r(r+5)} = \frac{r-5}{r(r+3)}$$
Выполним вычитание:
$$\frac{r-5}{r(r+3)}-\frac{r+5}{r(r-3)} = \frac{(r-5)(r-3)-(r+5)(r+3)}{r(r+3)(r-3)} = \frac{r^2-8r+15-(r^2+8r+15)}{r(r+3)(r-3)} = \frac{-16r}{r(r+3)(r-3)} = \frac{-16}{(r+3)(r-3)} = \frac{-16}{r^2-9}$$
Ответ: $$\frac{-16}{r^2-9}$$
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