I am not sure if the answer for the dividing rational expressions problem should be simplified $$ \frac{x}{x+2} \div \frac{1}{x^2 - 4} $$
-I am not sure if the answer for the problem (which is attached) would be $\frac{x^3-4x}{x+2}$ or if it could be simplified further.

You can simplify this in two ways.


*

*Dividing by a fraction is the same as multiplying by the flipped fraction, and if we do that we get
$$
\frac{x^2-4}{1}\cdot\frac{x}{x+2} = \frac{x(x^2-4)}{x+2}.
$$

*Next, we need to factor the bottom of the fraction. If you have enough practice with factoring you should recognize immediately that $x^2-4$ is a difference of squares. That is, $x^2-4=x^2-2^2$. So the expression is
$$
 \frac{x(x-2)(x+2)}{x+2}=x(x-2)
$$
after we cancel the $x+2$.

