Question

если
$\frac{x}{y} = 2$
найдите
$\frac{4y^{2 } - 3xy + x ^{2} }{x ^{2} - xy + y^{2} }$
​

Answer 1

$\displaystyle\bf\\\frac{x}{y} =2 \ \ \ \Rightarrow \ \ \ x=2y\\\\\\\frac{4y^{2} -3xy+x^{2} }{x^{2} -xy+y^{2} }=\frac{4y^{2} -3y\cdot 2y+(2y)^{2} }{(2y)^{2}-y\cdot 2y+y^{2} } =\frac{4y^{2}-6y^{2} +4y^{2} }{4y^{2}-2y^{2} +y^{2} } =\\\\\\=\frac{2y^{2} }{3y^{2} } =\frac{2}{3}$