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Given the following expression:
[tex]\frac{1-\frac{1}{x}}{3+\frac{1}{x}}[/tex]We will simplify the given expression as follows:
Multiply both the numerator and the denominator by x to eliminate the denominators of each part
[tex]\frac{1-\frac{1}{x}}{3+\frac{1}{x}}=\frac{x(1-\frac{1}{x})}{x(3+\frac{1}{x})}=\frac{x-x*\frac{1}{x}}{3x+x*\frac{1}{x}}=\frac{x-1}{3x+1}[/tex]So, the answer will be:
[tex]\frac{x-1}{3x+1}[/tex]