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, $x=3 / 7$