Given the functions
[tex]\begin{gathered} f(x)=x^2+4x-21 \\ g(x)\text{ = x-3} \end{gathered}[/tex]
To divide f(x) by g(x) implies
[tex]\frac{f(x)}{g(x)}=\frac{f}{g}(x)=\frac{x^2+4x-21}{x-3}[/tex]
Step 1
Factorize the numerator f(x)
[tex]\begin{gathered} x^2+4x-21 \\ \Rightarrow x^2+7x-3x-21 \\ x(x+7)-3(x+7) \\ \Rightarrow(x-3)(x+7) \end{gathered}[/tex]
Step 2
Divide the factorized numerator by the denominator
[tex]\begin{gathered} \frac{f(x)}{g(x)}=\frac{(x-3)(x+7)}{(x-3)} \\ \Rightarrow\frac{f}{g}(x)\text{ =}x+7 \end{gathered}[/tex]
Thus,
[tex]\frac{f}{g}(x)\text{ = x+7},\text{ x}\ne3[/tex]
The second option is the correct answer.
