Question

Вычислить x^2+xy-y^2/x^2-xy+y^2 при x/y=2

Answer 1

$\frac{x}{y} = 2 \\ x = 2y \\ \\ \frac{ {x}^{2} + xy - {y}^{2} }{ {x}^{2} - xy + {y}^{2} } = \frac{4 {y}^{2} + 2 {y}^{2} - {y}^{2} }{4 {y}^{2} - 2 {y}^{2} + {y}^{2} } = \frac{5 {y}^{2} }{3 {y}^{2} } = \frac{5}{3} = 1 \frac{2}{3}$