We have this two functions:
[tex]\begin{gathered} f(x)=3x+2 \\ g(x)=5x-6 \end{gathered}[/tex]We have to calculate what f/g is.
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{3x+2}{5x-6}[/tex]What is the domain of (f/g)(x)?
The domain is all the values of x for which the function has a defined value.
That means that if the denominator becames 0, the function is not defined.
This happens when 5x-6=0:
[tex]\begin{gathered} 5x-6=0 \\ 5x=6 \\ x=\frac{6}{5} \end{gathered}[/tex]Then, the domain is "all the real numbers different from 5/6".
