Question 194422

OK.  Complex fractions can be readily solved by first making the denominator of the complex fraction (in this case, (a+b)/6a^2b^4) equal to 1. We can do this by multiplying it by 6a^2b^4/(a+b).  When we do that, however, we have to also multiply the numerator of the complex fraction (in this case,(ab+b^2)/4ab^5) by 6a^2b^4/(a+b).  Why?  Because 6a^2b^4/(a+b)/6a^2b^4/(a+b) is equal to 1 and we do not change the complex fraction by multiplying it by 1.

Now, lets take a simple example: (a/b)/(c/d).  Multiply both the numberator and denominator by (d/c) and we get:(a/b)(d/c)/(c/d)(d/c)= (a/b)(d/c)/1=ad/bc.
Now, in your problem:
a=(ab+b^2)=b(a+b)
b=4ab^5
c=(a+b)
d=6a^2b^4
and
ad/bc=b(a+b)*6a^2b^4/4ab^5*(a+b)=
b*6a^2b^4/4ab^5 =6a^2b^5/4ab^5=(3/2)a  ---is that correct???


Hope this helps---ptaylor