Страница 36 номер 104, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение
Сократить дробь: 1) \(\frac{y - 16y^{\frac{1}{2}}}{5y^{\frac{1}{4}} + 20}\); 2) \(\frac{a^{\frac{4}{5}} - b^{\frac{4}{5}}}{a^{\frac{2}{5}} - b^{\frac{2}{5}}}\).
1) \(\frac{y - 16y^{\frac{1}{2}}}{5y^{\frac{1}{4}} + 20} = \frac{y^{\frac{1}{2}}\left(y^{\frac{1}{2}} - 16\right)}{5\left(y^{\frac{1}{4}} + 4\right)} = \frac{y^{\frac{1}{2}}\left(y^{\frac{1}{4}} - 4\right)\left(y^{\frac{1}{4}} + 4\right)}{5\left(y^{\frac{1}{4}} + 4\right)} = \frac{y^{\frac{1}{2}}\left(y^{\frac{1}{4}} - 4\right)}{5}\);
2) \(\frac{a^{\frac{4}{5}} - b^{\frac{4}{5}}}{a^{\frac{2}{5}} - b^{\frac{2}{5}}} = \frac{\left(a^{\frac{2}{5}} - b^{\frac{2}{5}}\right)\left(a^{\frac{2}{5}} + b^{\frac{2}{5}}\right)}{a^{\frac{2}{5}} - b^{\frac{2}{5}}} = a^{\frac{2}{5}} + b^{\frac{2}{5}}\).
