Question 144036
{{{ (x-(1/x)) / (x+1-(2/x))  =1}}}


Multiply both sides of your equation by the denominator on the left:


{{{ x-(1/x)=x+1-(2/x) }}}


Add {{{-x}}} to both sides:


{{{-(1/x)=1-(2/x)}}}


Add {{{-1}}} to both sides, and add {{{1/x}}} to both sides:


{{{-1=-(2/x)+(1/x)}}}


Combine the fractions:


{{{-1=-(1/x)}}}


Multiply both sides by {{{-x}}}:


{{{x=1}}}


Check:


{{{ (1-(1/1)) / (1+1-(2/1))  =1}}}


{{{0/0<>1}}}.  


Oops!  The single possible element in the solution set is NOT in the domain of the function on the right of your original equation. Therefore, the solution set for the given equation is empty.