Given:
[tex]\begin{gathered} f(x)=x^2+3x \\ g(x)=4-x \end{gathered}[/tex]Required:
To find (f/g)(x).
Explanation:
We know that
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]Now
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{x^2+3x}{4-x} \\ \\ =\frac{x(x+3)}{4-x} \end{gathered}[/tex]Final Answer:
[tex](\frac{f}{g})(x)=\frac{x(x+3)}{4-x}[/tex]