SOLUTION: simplify the complex fraction: {{{ (2+m-3/m)/(m/6 - 2/m)}}}

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Question 89644: simplify the complex fraction:
+%282%2Bm-3%2Fm%29%2F%28m%2F6+-+2%2Fm%29
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

simplify the complex fraction: 

+%282%2Bm-3%2Fm%29%2F%28m%2F6+-+2%2Fm%29

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


+%282%2F1%2Bm%2F1-3%2Fm%29%2F%28m%2F6+-+2%2Fm%29

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

+%28+%282%2F1%29%2B%28m%2F1%29-%283%2Fm%29+%29%2F%28+%28m%2F6%29-%282%2Fm%29+%29+++ 

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

The LCD of all those is 6m,
write that as %28%286m%29%2F1%29 and multiply every term
in both the top and the bottom by it:



Now cancel what will cancel and simplify:

%2812m%2B6m%5E2-18%29%2F%28m%5E2-12%29

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

%286m%5E2%2B12m-18%29%2F%28m%5E2-12%29

The top will factor by taking out a 6

%286%28m%5E2%2B2m-3%29%29%2F%28m%5E2-12%29

The top factors again,

%286%28m%2B3%29%28m-1%29%29%2F%28m%5E2-12%29

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

Edwin