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