Dividing functions
In order to divide a couple of functions, we simply divide their equations:
if f(x) = 25 - x²
and g(x) = x + 5
then
[tex]\begin{gathered} \frac{f}{g}(x)=\frac{f(x)}{g(x)} \\ \downarrow \\ \frac{f}{g}(x)=\frac{25-x^2}{x+5} \end{gathered}[/tex]
Simplifying the expression
In order to simplify the fraction we just factor the numerator:
25 - x² = (5 + x) (5 - x)
then
[tex]\frac{f}{g}(x)=\frac{(5+x)(5-x)}{x+5}[/tex]
Since
5 + x = x + 5
we can cancel this factor from the denominator:
then,
[tex]\frac{f}{g}(x)=5-x[/tex]
Answer: (f/g)(x) = 5 - x
