[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
For the given functions:
[tex]\begin{gathered} f(x)=x-3 \\ g(x)=\sqrt[]{x-3} \end{gathered}[/tex][tex]\begin{gathered} (\frac{f}{g})(x)=\frac{x-3}{\sqrt[]{x-3}} \\ \\ \text{Simplify:} \\ (\frac{f}{g})(x)=\frac{x-3}{\sqrt[]{x-3}}\cdot\frac{\sqrt[]{x-3}}{\sqrt[]{x-3}} \\ \\ (\frac{f}{g})(x)=\frac{x-3\cdot\sqrt[]{x-3}}{(\sqrt[]{x-3})^2} \\ \\ (\frac{f}{g})(x)=\frac{x-3\cdot\sqrt[]{x-3}}{x-3^{}} \\ \\ (\frac{f}{g})(x)=\sqrt[]{x-3} \end{gathered}[/tex]
