Answer
$ \displaystyle \frac{41}{24x} $
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad 2,3,x.$
List of factors of the second denominator: $\qquad 2,2,2,x$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $List$=2,3,x...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
( $x$ and one of the 2's are already in, we add the other two 2's to the list)
List = $2,3,x,2,2$
$LCD=24x$
Step 2. Rewrite each expression with the LCD:
$\displaystyle \frac{5}{6x}\cdot\frac{4}{4}+\frac{7}{8x}\cdot\frac{3}{3}=\frac{20}{24x}+\frac{21}{24x}=...$
Step 3. Combine numerators over the LCD
$=\displaystyle \frac{20+21}{24x}$
Step 4. Simplify, if possible.
=$ \displaystyle \frac{41}{24x} $
