SOLUTION: I need to simplify the complex fraction and reduce to lowest terms. ab+b^2 ------ 4ab^5 ------ a+b ------ 6a^2b^4

Question 327069: I need to simplify the complex fraction and reduce to lowest terms.
ab+b^2
------
4ab^5
------
a+b
------
6a^2b^4

Found 2 solutions by mananth, jessica43:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
ab+b^2
------
4ab^5
------
a+b
------
6a^2b^4

Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
((ab+b^2)/(4ab^5))/((a+b)/(6a^2b^4))
Dividing by a fraction is the same as multiplying by the fraction's reciprocal (the reciprocal is just the fraction flipped upside-down). So:
((ab+b^2)/(4ab^5))/((a+b)/(6a^2b^4))=
((ab+b^2)/(4ab^5))*((6a^2b^4)/(a+b))=
((ab+b^2)*(6a^2b^4))/((4ab^5)*(a+b))
Now you need to see if you can cancel anything in the numberator and the denominator. If you factor the numerator (factor out a b from the first term), you can cancel out the (a+b)from the num and denom:
((ab+b^2)*(6a^2b^4))/((4ab^5)*(a+b))=
((b)(a+b)*(6a^2b^4))/((4ab^5)*(a+b))=
((b)*(6a^2b^4))/(4ab^5)=
Now multiply out the numerator to see if that will enable you to cancel anything else out:
((b)*(6a^2b^4))/(4ab^5)=
(6a^2b^5)/(4ab^5)
Now cancel the b^5:
(6a^2)/(4a)
This can also be written as (6aa)/(4a), so you can cancel an a:
(6a)/4
This can be reduced to
3a/2
So your simplifed fraction is 3a/2.
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