Question

calcule o valor numérico da expressao fracionaria (x elevado a -1 + 1/y) elevado a - x sobre ( x - y) elevado a -1 para x = 1 e y = -1/2

Answer 1

$f(x,y)=\frac{(x^{-1}+\frac{1}{y})^{-x}}{(x-y)^-1}$

$f(1,-\frac{1}{2})=\frac{(1^{-1}+\frac{1}{-\frac{1}{2}})^{-1}}{(1-(-\frac{1}{2})^-1}$

$f(1,-\frac{1}{2})=\frac{(1-2)^{-1}}{(1+\frac{1}{2})^-1}$

$f(1,-\frac{1}{2})=\frac{(-1)^{-1}}{(\frac{3}{2})^-1}$

$f(1,-\frac{1}{2})=\frac{-1}{\frac{2}{3}}$

$\boxed{f(1,-\frac{1}{2})=\frac{-3}{2}}$