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МатематикаВопрос:
6) \(a-\frac{a^2}{a+1}\)\(\cdot\) \(\frac{a^2-1}{a^2+2a}\);
Ответ:
Преобразуем выражение:
- $$a-\frac{a^2}{a+1} = \frac{a(a+1)-a^2}{a+1} = \frac{a^2+a-a^2}{a+1} = \frac{a}{a+1}$$
- $$\frac{a^2-1}{a^2+2a} = \frac{(a-1)(a+1)}{a(a+2)}$$
Умножим первую дробь на вторую:
$$\frac{a}{a+1} \cdot \frac{(a-1)(a+1)}{a(a+2)} = \frac{a-1}{a+2}$$
Ответ: $$\frac{a-1}{a+2}$$
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