Question

Найдите значения выражений

Answer 1

$\displaystyle\bf\\\\\\\\\frac{y}{x} =6^{-1}=\\\\\\\frac{y}{x} =\frac{1}{6} \ \ \ \Rightarrow \ \ \ x=6y\\\\\\\frac{5x^{-1} -y^{-1} }{5x^{-1} +y^{-1} } =\frac{\dfrac{5}{x} -\dfrac{1}{y} }{\dfrac{5}{x}+\dfrac{1}{y} }=\frac{\dfrac{5y-x}{xy} }{\dfrac{5y+x}{xy} } =\frac{(5y-x)\cdot xy}{(5y+x)\cdot xy} =\frac{5y-6y}{5y+6y} =\\\\\\=\frac{-y}{11y} =-\frac{1}{11}$