The formula for the average rate of change between two points on a function is:

Since we want between:

We need to first calculate the values of the funciton in these points:
![\begin{gathered} f(x_1)=f(2)=\frac{\sqrt[]{2+2}}{2^2-3}=\frac{\sqrt[]{4}}{4-3}=(2)/(1)=2 \\ f(x_2)=f(7)=\frac{\sqrt[]{7+2}}{7^2-3}=\frac{\sqrt[]{9}}{49-3}=(3)/(46) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/aw29nvnhmgo9s3gijbue0mftqy5kwbyucy.png)
Now, we input these into the formula:

Thus, the average rate of change is -89/230.