Question

Помогите упростить выражение (5/а-а/5) *( 1/а-5+ 1/5+a)

Answer 1

$( \frac{5}{a} - \frac{a}{5} ) \times ( \frac{1}{a - 5} + \frac{1}{5 + a} ) = \\ ( \frac{25}{5a} - \frac{ {a}^{2} }{5a} ) \times ( \frac{5 + a}{( a - 5)(a + 5)} ) = \\ \frac{25 - {a}^{2} }{5a} \times \frac{5 + a}{(a - 5)(a + 5)} = \\ \frac{(5 - a)(5 + a)}{5a} \times \frac{5 + a}{(a - 5)(a + 5) } = \\ \frac{(5 - a)(5 + a)}{5a} = \frac{25 - {a}^{2} }{5a}$