Answer
$ \displaystyle \frac{2+9x}{x} $
Work Step by Step
$\displaystyle \frac{2}{x}+9=\frac{2}{x}+\frac{9}{1}$
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad x.$
List of factors of the second denominator: $\qquad 1$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $List$=x,...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
List = $x,1, $
$LCD=x$
Step 2. Rewrite each expression with the LCD:
$\displaystyle \frac{2}{x}+\frac{9}{1}\cdot\frac{x}{x}=\frac{2}{x}+\frac{9x}{x}=...$
Step 3. Combine numerators over the LCD
$= \displaystyle \frac{2+9x}{x} $
Step 4. Simplify, if possible.
... nothing to simplify
=$ \displaystyle \frac{2+9x}{x} $
