a. \( \frac{8}{m+5} \cdot m \)

To simplify the expression \( \frac{8}{m+5} \cdot m \), you can think of it as multiplying \( m \) by the fraction. This can be rearranged as \( \frac{8m}{m+5} \). It's a straightforward simplification, but what makes it more interesting is how you could apply this in real-world situations, such as calculating rates or proportions related to physical quantities. When using this expression in equations, a common mistake is forgetting that \( m \) cannot equal \(-5\) because that would make the denominator zero! Always check your restrictions and be mindful of the values you can and cannot substitute into the equation.