Answer
$\displaystyle \frac{37}{18x}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad 3,3,x.$
List of factors of the second denominator: $\qquad 2,3,x$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $List$=3,3,x...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
($3$ and $x$ are already in, we add 2 to the list)
List = $3,3,x,2$
$LCD=18x$
Step 2. Rewrite each expression with the LCD:
$\displaystyle \frac{2}{9x}\cdot\frac{2}{2}+\frac{11}{6x}\cdot\frac{3}{3}=\frac{4}{18x}+\frac{33}{18x}=...$
Step 3. Combine numerators over the LCD
$=\displaystyle \frac{4+33}{18x}$
Step 4. Simplify, if possible.
$=\displaystyle \frac{37}{18x} \qquad$... nothing to simplify.