If x+frac{1}{y}=1 and y+frac{1}{z}=1,then fin | vedclass

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(B) Given equations are $x+\frac{1}{y}=1$ and $y+\frac{1}{z}=1$.From the first equation,$x=1-\frac{1}{y} = \frac{y-1}{y}$.Therefore,$\frac{1}{x} = \fr

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$1$

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(B) Given equations are $x+\frac{1}{y}=1$ and $y+\frac{1}{z}=1$.From the first equation,$x=1-\frac{1}{y} = \frac{y-1}{y}$.Therefore,$\frac{1}{x} = \frac{y}{y-1}$.From the second equation,$\frac{1}{z} = 1-y$.Therefore,$z = \frac{1}{1-y}$.Now,substitute these into the expression $z+\frac{1}{x}$:$z+\frac{1}{x} = \frac{1}{1-y} + \frac{y}{y-1}$.Since $y-1 = -(1-y)$,we can write:$z+\frac{1}{x} = \frac{1}{1-y} - \frac{y}{1-y} = \frac{1-y}{1-y} = 1$.

If $x+\frac{1}{y}=1$ and $y+\frac{1}{z}=1$,then find the value of $z+\frac{1}{x}$.

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