Question 75085
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{{{(4+2/x)/(x/4+1/8)}}}

Write the {{{4}}} as {{{4/1}}} so everything
will be a fraction.

{{{(4/1+2/x)/(x/4+1/8)}}}

Then put parentheses around the top and the bottom:

{{{((4/1+2/x))/((x/4+1/8))}}}

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

The LCD of those is 8x, so multiply by the
fraction {{{8x/(8x)}}} but write it as
{{{(8x/1)/(8x/1)}}}

So now we have

{{{(8x/1)/(8x/1)}}}·{{{((4/1+2/x))/((x/4+1/8))}}}

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

{{{((8x/1)(4/1)+(8x/1)(2/x))/((8x/1)(x/4)+(8x/1)(1/8))))}}}

Cancel what will cancel and you have:

{{{(32x+16)/(2x^2+x)}}}

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

{{{(16(2x+1))/(x(2x+1))}}}

Cancel the {{{(2x+1))}}}'s and all that's left is

{{{16/x}}}

Edwin</pre></b></font>