Question

Спростіть вираз:
($\frac{a+7}{a-7}$ - $\frac{a-7}{a+7}$) ÷ $\frac{14}{a^{2}-7a }$

Answer 1

Ответ:

$\frac{2a^{2}}{a+7}$

Объяснение:

$(\frac{a+7}{a-7} - \frac{a - 7}{a + 7} ) : \frac{14}{a^{2} - 7a} = \\\\= (\frac{(a+7)(a + 7)}{(a-7)(a + 7)} - \frac{(a - 7)(a - 7)}{(a + 7)(a - 7)} ) \cdot \frac{a^{2} - 7a}{14} = \\\\= \frac{(a+7)^{2} - (a - 7)^{2}}{(a-7)(a + 7)} \cdot \frac{a (a - 7)}{14} = \\\\= \frac{a^{2} + 14a + 49 - a^{2} + 14a - 49}{(a-7)(a + 7)} \cdot \frac{a (a - 7)}{14} \\\\= \frac{28a}{(a-7)(a+7)} \cdot \frac{a (a - 7)}{14} = \\\\= \frac{28a}{a+7} \cdot \frac{a}{14} = \frac{2a}{a+7} \cdot \frac{a}{1} = \frac{2a^{2}}{a+7}$