Question 768626
Not sure if you mean what you wrote, {{{(3/x-2) + 1/2 = (x/x-2)}}}, or something else like maybe {{{3/(x-2)+1/2=x/(x-2)}}}.
(EDIT: SEE MUCH LOWER DOWN, THE EQUATION YOU REALLY WANTED HELP WITH.)


Using exactly what you wrote, {{{(3/x-2) + 1/2 = (x/x-2)}}}, multiply both members by x.
{{{3-2x+x/2=x-2x}}}
{{{3+x/2=x}}}
{{{3=x-x/2}}}
{{{3=x/2}}}
{{{x=6}}}



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THIS IS THE EQUATION YOU REALLY WANTED TO SHOW:
{{{3/(x-2)+1/2=x/(x-2)}}}
The simplest common denominator is 2*(x-2), so multiply both members by this product.


{{{ 2(x-2)(3/(x-2))+(2(x-2))(1/2)=2(x-2)(x/(x-2))}}}
You can find what factors between numerators and denominators cancel,...
{{{2*3+x-2=2x}}}
{{{6-2=x}}}
FINAL ANSWER: {{{highlight(x=4)}}}