Question 106011
The given problem can be written as:


{{{ 2+(1/(1-(1/x))) over 2-(3/(1-(1/x))) }}}


We first take the LCM of the terms that are present as the denominators in the entire expression. So that gives us. 


{{{ ((2 + (x/(x-1))) / (2 - (3x/(x - 1))) )}}}


Again taking LCM, we get:


{{{((2(x-1) + x)/(x - 1))/((2(x-1) - 3x)/(x-1))}}} 


Here the (x - 1) term cancels out. So we get: 


{{{((2x - 2 + x)/(2x - 1 - 3x))}}} 


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


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



thus the solution.