Answer:
[tex](\frac{f}{g} )(x)=5-x[/tex]
Step-by-step explanation:
If [tex]f(x)=25-x^2[/tex] and [tex]g(x)=x+5[/tex]
Then [tex](\frac{f}{g} )(x)=\frac{25-x^2}{x+5}[/tex]
We can factor out the numerator to get
[tex](\frac{f}{g} )(x)=\frac{(5-x)(5+x)}{x+5}[/tex]
And thanks to the communicative property of addition, [tex]5+x=x+5[/tex]
This means that the x+5 on both the top and the bottom cancel out. This leaves you with
[tex](\frac{f}{g} )(x)=5-x[/tex]
