Dividing algebraic fractions

2p/4p^2 divided by 6p^3/6p+3

To multiply two fractions, you multiply the numerators together and you multiply the denominators together
= 2p(6p + 3) / 6p^3(4p^2 - 1)

Next, we can factor out a 3 in the numerator
= 6p(2p + 1) / 6p^3(4p^2 - 1)

Next, we can factor the denominator
= 6p(2p + 1) / 6p^3(2p - 1)(2p + 1)

Since we have (2p + 1) in the top and bottom, we can cancel it
= 6p / 6p^3(2p - 1)

We can also cancel a 6p in the top and bottom
1 / p^2(2p - 1)

hope I helped