If x+frac{1}{y}=1 and y+frac{1}{z}=1, find th | 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}=\frac{y

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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,$\frac{1}{z}=1-y.$Thus,$z=\frac{1}{1-y}.$Now,substitute these into the expression $z+\frac{1}{x}$:$z+\frac{1}{x} = \frac{1}{1-y} + \frac{y}{y-1}$$= \frac{1}{1-y} - \frac{y}{1-y}$$= \frac{1-y}{1-y} = 1.$

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

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