Question

(x^-1+y^-1)^2×(x+y)^-2​

Answer 1

Ответ:

$\frac{1}{ {x}^{2} {y}^{2} }$

Пошаговое объяснение:

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