algebra help please?

Question

how do i perform the indicated operations, and reduce answer to lowest terms

p^3 +8q^3 p^2 -2pq+4q^2
_______ / ___________ (division divided by a division)
p^2 -4q^2 3p^2 -7pq+2q^2

^ means to the # power
thank you

Answer 1

redwrite the problem as a multiplication problem

(p^3 + 8q^3 / p^2 - 4q^2) ( 3p^2 - 7pq + 2q^2 / p^2 - 2pq + 4q^2)

factor each of the fractions completely

(p + 2q)(p^2 - 2pq + 4q^2)/ ( p - 2q ) ( p + 2q) * ( 3p - q ) ( p - 2q ) / ( p^2 -2pq + 4q^2)

numerator times numerator and denominator times denominator
and divide out common terms

(3p - q ) is the answer you should get

Answer 2

((p^3 + 8q^3)/(p^2 - 4q^2))
----------------------------------------------------
((p^2 - 2pq + 4q^2)/(3p^2 - 7pq + 2q^2))

(((p + 2q)(p^2 - 2pq + 4q^2))/((p - 2q)(p + 2q)))
------------------------------------------------------------
((p^2 - 2pq + 4q^2)/((3p - q)(p - 2q)))

((p^2 - 2pq + 4q^2)/(p - 2q)) / ((p^2 - 2pq + 4q^2)/((3p - q)(p - 2q)))

((p^2 - 2pq + 4q^2)/(p - 2q)) * (((3p - q)(p - 2q))/(p^2 - 2pq + 4q^2))

((3p - q)(p - 2q)(p^2 - 2pq + 4q^2))/((p - 2q)(p^2 - 2pq + 4q^2))

ANS : 3p - q