How do you solve #\frac { 1} { 5- \frac { 1} { 1- \frac { 1} { x } } } = \frac { 2} { 7}#?

This is kind of a mess, but as long as we take it step by step, we'll be fine

#1/(5-1/(1-1/(x)))=2/7#

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Let's make #1-1/x# one fraction with a common denominator

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#1/(5-1/((x-1)/x))=2/7#

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Now, let's change this mess of #1/((x-1)/x)# to #x/(x-1)#

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#1/(5-x/(x-1))=2/7#

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Now, if we change #5# to #5/1#, we can give it the same denominator: #(5x-5)/(x-1)#

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That gives us

#1/((5x-5-x)/(x-1))=2/7#

or

#(x-1)/(4x-5)=2/7#

See how much better this looks!! We are almost there

Let's clear the denominator

#7x-7=8x-10#

#x=3#

There! We are done, good work