Question 174308
I think you are trying to illustrate the following:


{{{((4ab^5)/(a+b))/(6a^2b^4)}}}


Since you aren't trying to find the sum of fractions, you have no need of a Lowest Common Denominator.


So, this is {{{(4ab^5)/(a+b)}}} divided by {{{6a^2b^4}}}, but the divisor can be expressed as {{{(6a^2b^4)/1}}}.


Just like performing any other division by a fraction problem, invert the divisor and multiply:


{{{((4ab^5)/(a+b))(1/6a^2b^4)=(4ab^5)/((a+b)(6a^2b^4))}}} 


Now, all you need to do is eliminate factors common to both the numerator and denominator, namely {{{2ab^4}}}, leaving you with:


{{{(2b)/((a+b)(3a))}}} which can be expressed as {{{2b/(3a^2+3ab)}}}.  It is moot, in my mind, as to which form is simpler.  In fact, if this were the result of an intermediate calculation as part of a larger problem, you may choose one over the other depending on the nature of the further calculation in which you intend to use the expression.