Question 89644
<pre><font size = 5 color = "red"><b>
simplify the complex fraction: 

{{{ (2+m-3/m)/(m/6 - 2/m)}}}

Put 1 under the 2 and the m so that
everything will be fractions:


{{{ (2/1+m/1-3/m)/(m/6 - 2/m)}}}

Put parentheses around every fraction in the
top and in the bottom:

{{{ ( (2/1)+(m/1)-(3/m) )/( (m/6)-(2/m) )   }}} 

Look at all the denominators top 
and bottom: {{{1}}},{{{1}}},{{{m}}},{{{6}}},{{{m}}}

The LCD of all those is {{{6m}}},
write that as {{{((6m)/1)}}} and multiply every term
in both the top and the bottom by it:

{{{( ((6m)/1)(2/1)+((6m)/1)(m/1)-((6m)/1)(3/m))/( ((6m)/1)(m/6)-((6m)/1)(2/m))}}}

Now cancel what will cancel and simplify:

{{{(12m+6m^2-18)/(m^2-12)}}}

That's probably as far as you need to go. You can
arrange the numerator in descending order of powers
of x.

{{{(6m^2+12m-18)/(m^2-12)}}}

The top will factor by taking out a 6

{{{(6(m^2+2m-3))/(m^2-12)}}}

The top factors again,

{{{(6(m+3)(m-1))/(m^2-12)}}}

But since the bottom does not factor, there was
no need to factor the top, because nothing
cancels.

Edwin</pre>