Сократите дробь:
а) $\frac{x^2 - 2}{x + \sqrt{2}}$;
б) $\frac{\sqrt{5} - a}{5 - a^2}$;
в) $\frac{\sqrt{x} - 5}{25 - x}$;
г) $\frac{\sqrt{2} + 2}{\sqrt{2}}$;
д) $\frac{5 + \sqrt{10}}{\sqrt{10}}$;
е) $\frac{2\sqrt{3} - 3}{5\sqrt{3}}$.
$\frac{x^2 - 2}{x + \sqrt{2}} = \frac{(x - \sqrt{2})(x + \sqrt{2})}{x + \sqrt{2}} = x - \sqrt{2}$
$\frac{\sqrt{5} - a}{5 - a^2} = \frac{\sqrt{5} - a}{(\sqrt{5} - a)(\sqrt{5} + a)} = \frac{1}{\sqrt{5} + a}$
$\frac{\sqrt{x} - 5}{25 - x} = -\frac{\sqrt{x} - 5}{x - 25} = -\frac{\sqrt{x} - 5}{(\sqrt{x} - 5)(\sqrt{x} + 5)} = -\frac{1}{\sqrt{x} + 5}$
$\frac{\sqrt{2} + 2}{\sqrt{2}} = \frac{\sqrt{2}(1 + \sqrt{2})}{\sqrt{2}} = 1 + \sqrt{2}$
$\frac{5 + \sqrt{10}}{\sqrt{10}} = \frac{\sqrt{5} * \sqrt{5} + \sqrt{5} * \sqrt{2}}{\sqrt{5} * \sqrt{2}} = \frac{\sqrt{5}(\sqrt{5} + \sqrt{2})}{\sqrt{5} * \sqrt{2}} = \frac{\sqrt{5} + \sqrt{2}}{\sqrt{2}}$
$\frac{2\sqrt{3} - 3}{5\sqrt{3}} = \frac{2\sqrt{3} - \sqrt{3} * \sqrt{3}}{5\sqrt{3}} = \frac{\sqrt{3}(2 - \sqrt{3})}{5\sqrt{3}} = \frac{2 - \sqrt{3}}{5}$
Пожауйста, оцените решение
