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$\dfrac{1}{ 1+ \dfrac{1}{1- \frac{1}{ x}}}=4, x=?$
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We can follow outside to inside method to solve this type of problems. $x$ is in the inner part of this fraction; then, we need to
narrow the circle to reach $x$ :
$1 /(1+1 /(1-1 / x))=4$
This means that $(1+1 /(1-1 / \mathrm{x}))$ is equal to $1 / 4$. Then,
$1+1 /(1-1 / x)=1 / 4$
$1 /(1-1 / x)=1 / 4-1$
$1 /(1-1 / x)=-3 / 4$
This means that $1-1 / x=-4 / 3$. Then,
$1-1 / x=-4 / 3$
$1+4 / 3=1 / x$
$1 / x=7 / 3$
So, $x=3 / 7$
ago by Diamond (78,880 points)

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