SIMPLIFY:p^2+pq-6q^2/p^2-3pq+2q^2
want to understand how to solve it
well,
p^2+pq-6q^2 = (p+3q)(p-2q)
p^2-3pq+2q^2 = (p-q)(p-2q)
So, what cancels?
To simplify the expression (p^2 + pq - 6q^2) / (p^2 - 3pq + 2q^2), we can factor both the numerator and the denominator and then cancel out any common factors.
First, factor the numerator:
p^2 + pq - 6q^2
This expression cannot be further factored since the coefficients in front of the variables are not the same.
Next, factor the denominator:
p^2 - 3pq + 2q^2
This expression can be factored as (p - q)(p - 2q).
Now, we can rewrite the expression:
(p^2 + pq - 6q^2) / (p^2 - 3pq + 2q^2) = (p^2 + pq - 6q^2) / [(p - q)(p - 2q)]
To simplify further, we can cancel out any common factors between the numerator and the denominator. In this case, there are no common factors that can be canceled out.
Therefore, the simplified expression is:
(p^2 + pq - 6q^2) / (p^2 - 3pq + 2q^2)