Question

I need help on simplifying a rational expression
p^3+p^2q-2pq^2 divided by pq^2+p^2q-2p^3

Answer 1

\[\frac{p^3+p^2q-2pq^2}{pq^2+p^2q-2p^3}=\frac{p(p^2+pq-2q^2)}{p(q^2+pq-2p^2)}=\frac{p^2+pq-2q^2}{q^2+pq-2p^2}\]
Try factoring

Answer 2

thats what I need help on I don't know how to factor it

Answer 3

\[\begin{align*}(p-q)(p+2q)&=p(p+2q)-q(p+2q)\\&=p^2+2pq-pq-2q^2\\&=p^2+pq-2q^2\end{align*}\]
The denominator can be factored almost exactly the same way:
\[(q-p)(q+2p)=q^2+pq-2p^2\]
So
\[\frac{p^2+pq-2q^2}{q^2+pq-2p^2}=\frac{(p-q)(p+2q)}{(q-p)(q+2p)}=-\frac{(p-q)(p+2q)}{(p-q)(q+2p)}=-\frac{p+2q}{q+2p}\]

Answer 4

alright thnaks for the help it was really helpful

Answer 5

yw