Answer :
Assuming that x≠0 we get that:
[tex]\frac{1-\frac{1}{x}}{3+\frac{1}{x}}=\frac{1-\frac{1}{x}}{3+\frac{1}{x}}*\frac{x}{x}.[/tex]Simplifying the above result we get:
[tex]\frac{1-\frac{1}{x}}{3+\frac{1}{x}}*\frac{x}{x}=\frac{(1-\frac{1}{x})*x}{(3+\frac{1}{x})*x}.[/tex]Applying the distributive property we get:
[tex]\frac{(1-\frac{1}{x})*x}{(3+\frac{1}{x})*x}=\frac{x-1}{3x+1}.[/tex]Therefore:
[tex]\frac{1-\frac{1}{x}}{3+\frac{1}{x}}=\frac{x-1}{3x+1}.[/tex]Answer:
[tex]\begin{equation*} \frac{x-1}{3x+1}. \end{equation*}[/tex]