Answer
$ \displaystyle \frac{3x+1}{x} $
Work Step by Step
$3+\displaystyle \frac{1}{x}=\frac{3}{1}+\frac{1}{x}$
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad 1.$
List of factors of the second denominator: $\qquad x$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $List$=1,...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
( add $x $ to the list)
List = $1,x, $
$LCD=x$
Step 2. Rewrite each expression with the LCD:
$\displaystyle \frac{3}{1}\cdot\frac{x}{x}+\frac{1}{x}=\frac{3x}{x}+\frac{1}{x}=...$
Step 3. Combine numerators over the LCD
$= \displaystyle \frac{3x+1}{x} $
Step 4. Simplify, if possible.
... nothing to simplify
=$ \displaystyle \frac{3x+1}{x} $
