Recall that:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)},[/tex]
and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.
If f(x)=5x+3 and g(x)=4x-5 we get that:
[tex]\frac{f}{g}(x)=\frac{5x+3}{4x-5}\text{.}[/tex]
The domain of the above rational function is:
[tex]\begin{gathered} \mleft\lbrace x|g(x)\ne0\mright\rbrace=\lbrace x|4x-5\ne0\rbrace \\ =\lbrace x|4x\ne5\rbrace=\lbrace x|x\ne\frac{5}{4}\rbrace\text{.} \end{gathered}[/tex]
Answer: Last option.
