How do you simplify $\frac{y}{y-\frac{y}{y+\frac{1}{y}}}$ ?

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Answer 1 · 2017-11-09T07:32:28

$"The Exp.="(y^2+1)/(y^2-y+1).$

For ease of writing, let, $x=y/(y+1/y),$ so that, the given

Expression (Exp.) becomes,

Exp. $=y/(y-x).........(star).$

Now, $x=y/(y+1/y)=y/{(y^2+1)/y}=y^2/(y^2+1).$

$:. y-x=y-y^2/(y^2+1)={y(y^2+1)-y^2}/(y^2+1).$

$rArr y-x={y(y^2+1-y)}/(y^2+1).$

Therefore, the Exp. = $y/(y-x)=y-:1/(y-x),$

$=y-:{y(y^2+1-y)}/(y^2+1),$

$=cancel(y)xx(y^2+1)/{cancel(y)(y^2+1-y)}.$

$rArr" The Exp.="(y^2+1)/(y^2-y+1).$

How do you simplify \frac{y}{y-\frac{y}{y+\frac{1}{y}}}\frac{y}{y-\frac{y}{y+\frac{1}{y}}}?