# Simplify `((p^2-9q^2)/(2pq +6q^2))divide((3p^2-8pq-3q^2)/(3pq+q^2))` `Thanks<br>` ` ` ` ` ` ` ` ` ` ` ` `

*print*Print*list*Cite

Expert Answers

jeew-m | Certified Educator

`[(p^2-9q^2)/(2pq+6q^2)]/[(3p^2-8pq-3q^2)/(3pq+q^2)]`

`= (p^2-9q^2)/(2pq+6q^2)xx(3pq+q^2)/(3p^2-8pq-3q^2)`

`p^2-9q^2 = p^2-(3q)^2 = (p-3q)(p+3q)`

`3p^2-8pq-3q^2`

`= 3p^2-9pq+pq-3q^2`

`= 3p(p-3q)+q(p-3q)`

`= (p-3q)(3p+q)`

`= (p^2-9q^2)/(2pq+6q^2)xx(3pq+q^2)/(3p^2-8pq-3q^2)`

`= ((p+3q)(p-3q))/(2q(p+3q))xx(q(3p+q))/((p-3q)(3p+q))`

= 1/2

** So the simplified answer is **`1/2`