SOLUTION: how do you simplify the complex fraction {{{(4+2/x)/(x/4+1/8)}}}

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Question 75085: how do you simplify the complex fraction
%284%2B2%2Fx%29%2F%28x%2F4%2B1%2F8%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%284%2B2%2Fx%29%2F%28x%2F4%2B1%2F8%29

Write the 4 as 4%2F1 so everything
will be a fraction.

%284%2F1%2B2%2Fx%29%2F%28x%2F4%2B1%2F8%29

Then put parentheses around the top and the bottom:

%28%284%2F1%2B2%2Fx%29%29%2F%28%28x%2F4%2B1%2F8%29%29

The four denominators are 1, x, 4, and 8

The LCD of those is 8x, so multiply by the
fraction 8x%2F%288x%29 but write it as
%288x%2F1%29%2F%288x%2F1%29

So now we have

%288x%2F1%29%2F%288x%2F1%29·%28%284%2F1%2B2%2Fx%29%29%2F%28%28x%2F4%2B1%2F8%29%29

Now remove the parentheses by distributing on the 
top and bottom:



Cancel what will cancel and you have:

%2832x%2B16%29%2F%282x%5E2%2Bx%29

Now factor 16 out of the top and x out of the bottom:

%2816%282x%2B1%29%29%2F%28x%282x%2B1%29%29

Cancel the %282x%2B1%29%29's and all that's left is

16%2Fx

Edwin