Question

Буду вдячна за обгрунтовано відповідь.​

Answer 1

Ответ:

$( \frac{x + 4y}{ {x}^{2} - 4xy} - \frac{x - 4y}{ {x}^{2} + 4xy } ) \div \frac{4 {y}^{2} }{16 {y}^{2} - {x}^{2} } = \frac{x(x + 4y)(x + 4) - x(x - 4y)(x - 4)}{ {x}^{2} ({x}^{2} - 16 {y}^{2}) } \div \frac{4 {y}^{2} }{16 {y}^{2} - {x}^{2} } = \frac{ x(x + 4y)(x + 4) - x(x - 4y)(x - 4)}{ {x}^{2} ( x - 4y)(x + 4y) } \div \frac{4 {y}^{2} }{(4y - x)(4y + x)} = \frac{ {x}^{2} + 4xy + {x}^{2} + 4x - {x}^{2} + 4xy - {x}^{2} + 4x }{ {x}^{2} (x - 4y)(x + 4y)} \times \frac{ - (x - 4y)(4y + x)}{4 {y}^{2} } = - \frac{8x (y + 1)}{4 {x}^{2} {y}^{2} } = - \frac{2y + 2}{x {y}^{2} }$