Question

Ajudem Por favor!!!!! :(

Qual é o valor numérico da expressão abaixo, para x = 0,45222... e y =
0,31888... ?

Answer 1

Explicação passo-a-passo:

• $\sf x=0,45222...=\dfrac{452-45}{900}=\dfrac{407}{900}$

• $\sf y=0,31888...=\dfrac{318-31}{900}=\dfrac{287}{900}$

Temos que:

$\sf \dfrac{\frac{1}{y}}{1-\frac{1}{1+\frac{1}{x}}}$

$\sf =\dfrac{\frac{1}{\frac{287}{900}}}{1-\frac{1}{1+\frac{1}{\frac{407}{900}}}}$

$\sf =\dfrac{\frac{900}{287}}{1-\frac{1}{1+\frac{900}{407}}}$

$\sf =\dfrac{\frac{900}{287}}{1-\frac{1}{\frac{407+900}{407}}}$

$\sf =\dfrac{\frac{900}{287}}{1-\frac{1}{\frac{1307}{407}}}$

$\sf =\dfrac{\frac{900}{287}}{1-\frac{407}{1307}}$

$\sf =\dfrac{\frac{900}{287}}{\frac{1307-407}{1307}}$

$\sf =\dfrac{\frac{900}{287}}{\frac{900}{1307}}$

$\sf =\dfrac{900}{287}\cdot\dfrac{1307}{900}$

$\sf =\red{\dfrac{1307}{287}}$