Question 981683
What you really have is ambiguous.  The spacing in your text suggests you may actually have   {{{18/(x-2)=4/3}}}.


Multiply members by the LCD,  {{{3(x-2)}}}...


{{{18*3*(x-2)/(x-2)=3(x-2)(4/3)}}}


{{{18*3=(x-2)*4}}}
{{{(18*3)/4=x-2}}}
{{{x=(18*3)/4+2}}}
{{{x=13&1/2+2}}}
{{{highlight(x=15&1/2)}}}--------I believe no mistakes made.  You can check this solution by using the value in the given equation, the one I solved.  Find if it works.



Did you really have by some chance,  {{{18/x-2=4/3}}} ?
(Reported, that NO.  The first form solved was what was intended)
The following was not needed:
-
{{{18/x=4/3+6/3}}}


{{{18/x=10/3}}}


{{{x/18=3/10}}}


{{{x=(3/10)*18}}}


{{{x=(3/5)*9}}}


{{{x=27/5}}}


{{{highlight(x=5&2/5)}}}