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МатематикаВопрос:
6) \(p-\frac{5p}{p+2}\):\(\frac{p-3}{p+2}\);
Ответ:
Преобразуем выражение:
- $$p-\frac{5p}{p+2} = \frac{p(p+2)-5p}{p+2} = \frac{p^2+2p-5p}{p+2} = \frac{p^2-3p}{p+2} = \frac{p(p-3)}{p+2}$$
Разделим первую дробь на вторую:
$$\frac{p(p-3)}{p+2}:\frac{p-3}{p+2} = \frac{p(p-3)}{p+2} \cdot \frac{p+2}{p-3} = p$$
Ответ: p
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