m^2-m-6 m^2

_________ x ______

m^2-9 m^2+2m

To simplify the given expression:

(m^2 - m - 6) / (m^2 - 9) * (m^2) / (m^2 + 2m)

First, let's factor both the numerator and denominator to see if any terms can be canceled out.

Numerator:
m^2 - m - 6

The expression can be factored as (m - 3)(m + 2).

Denominator:
m^2 - 9

The denominator is a difference of squares and can be factored as (m - 3)(m + 3).

Now, let's rewrite the expression with the factored terms:

((m - 3)(m + 2)) / ((m - 3)(m + 3)) * (m^2) / (m^2 + 2m)

Next, we can cancel out the common factors between the numerator and denominator:

(m - 3) / (m + 3) * (m^2) / (m^2 + 2m)

Finally, let's simplify the expression further:

(m * (m - 3)) / (m * (m + 2)) * (m^2) / (m * (m + 2))

After canceling out the common factors, we end up with:

(m - 3) / (m + 2) * m

So, the simplified expression is:

m * (m - 3) / (m + 2)