Respuesta:
[tex]\frac{y}{x}[/tex] ; La correcta es la opción b )
Explicación paso a paso:
[tex]1-\frac{1}{1-\frac{1}{1-\frac{x}{y} } } = 1-\frac{1}{1-\frac{1}{\frac{y-x}{y} } } =1-\frac{1}{1-\frac{y}{y-x} } =1-\frac{1}{\frac{y-x-y}{y-x} }[/tex]
[tex]= 1-\frac{y-x}{y-x-y} = 1-\frac{y-x}{-x} = 1+\frac{y-x}{x} =\frac{x+y-x}{x}[/tex]
[tex]= \frac{y}{x}[/tex]
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Respuesta:
[tex]\frac{y}{x}[/tex] ; La correcta es la opción b )
Explicación paso a paso:
[tex]1-\frac{1}{1-\frac{1}{1-\frac{x}{y} } } = 1-\frac{1}{1-\frac{1}{\frac{y-x}{y} } } =1-\frac{1}{1-\frac{y}{y-x} } =1-\frac{1}{\frac{y-x-y}{y-x} }[/tex]
[tex]= 1-\frac{y-x}{y-x-y} = 1-\frac{y-x}{-x} = 1+\frac{y-x}{x} =\frac{x+y-x}{x}[/tex]
[tex]= \frac{y}{x}[/tex]