Question 59770
The best way to solve complex fractions is to:
First, try to factor as much as possible
Second, try to eliminate denominators by multiplying each fraction (top and bottom) by a common denominator.
Third, continue to simplify or re-factor if possible.
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1. {{{((4 + 2/x)/ (x/3+1/6) )}}} [No factoring involved]

{{{(((18x)(4/1 + 2/x))/ ((18x)(x/3+1/6)) )}}}[Find the common denominator (18x)]
{{{((72x+36)/ (6x^2+3x) )}}} [Cancel wherever necessary]
{{{(  ((9)(8x+4))/ ( (3x)(2x+1) ) )}}}[In this case you can re-factor]
{{{( ((3)(8x+4))/ ((1x)(2x+1)) )}}} [Cancel wherever necessary]
{{{( (24x+12)/ (2x^2+x) )}}} [Simplify]
{{{( ((12)(2x+1))/( (x)(2x+1)) )}}} [Re-factor again]
{{{( ((12)(2x+1))/( (x)(2x+1)) )}}} [Cancel again]
12/x [final answer]

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2.){{{( (1/(K+2))/(5/(K^2-4)) )}}} 
{{{((1/(K+2))/(5/((K-2))(K+2))))}}} [Factor wherever possible]
{{{((K+2)(1/(K+2))/(K+2)(5/((K-2))(K+2))))}}}[Find the common denominator ((K+2)]
{{{((1)/(5/(K-2)))))}}}[Cancel wherever possible]
{{{( (1)(((K-2)/5)))}}} [Flip the denominator and multiply]
{{{((K-2)/5)))}}}[final answer]