Question

Помогите пожалуйста ​

Answer 1

Ответ:

$\frac{2022}{8172925}$

Объяснение:

$\frac{ \frac{a}{a + b} - \frac{a - b}{a} }{ \frac{a - b}{a + b} + \frac{b}{a} } \div ( \frac{b}{a {}^{2} + b {}^{2} } ) = \\ = \frac{ \frac{a {}^{2} - (a - b)(a + b)}{a(a + b)} }{ \frac{a(a - b) + b(a + b)}{a(a + b)} } \div ( \frac{b}{a {}^{2} + b {}^{2} } ) = \\ = \frac{a {}^{2} - (a - b)(a + b)}{a(a - b) + b(a + b)} \times \frac{a {}^{2} + b {}^{2} }{b} = \\ = \frac{a {}^{2} - (a {}^{2} - b {}^{2}) }{(a(a - b) + b(a + b))b} = \\ = \frac{a {}^{2} - a {}^{2} + b {}^{2} }{(a(a - b) + b(a + b))b} = \\ = \frac{b}{ a(a - b) + b(a + b)} = \\ = \frac{b}{a {}^{2} - ab + ab + b {}^{2} } = \\ = \frac{b}{a {}^{2} + b {}^{2} }$

$\frac{b}{a {}^{2} + b {}^{2} } = \frac{2022}{(2021) {}^{2} + (2022) {}^{2} } = \frac{2022}{4084441 + 4088484} = \frac{2022}{8172925}$