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МатематикаВопрос:
06.6. a) \(\frac{1+c^3}{1+c}-c\)\(\cdot\) \(\frac{1+c}{1-c^2}\);
Ответ:
Преобразуем выражение:
- $$\frac{1+c^3}{1+c}-c = \frac{(1+c)(1-c+c^2)}{1+c}-c = 1-c+c^2-c = 1-2c+c^2 = (1-c)^2$$
- $$\frac{1+c}{1-c^2} = \frac{1+c}{(1-c)(1+c)} = \frac{1}{1-c}$$
Умножим первую дробь на вторую:
$$(1-c)^2 \cdot \frac{1}{1-c} = 1-c$$
Ответ: 1-c
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