Answer
$\displaystyle \frac{7x-18}{x(x-6)}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad x$
List of factors of the second denominator: $\qquad (x-6)$
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
($(x-6)$ is added to the list)
List = $x,(x-6), $
$LCD=x(x-6)$
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{3}{x}\cdot\frac{(x-6)}{(x-6)}+\frac{4}{(x-6)}\cdot\frac{x}{x}= \displaystyle \frac{3(x-6)}{x(x-6)}+\frac{4x}{x(x-6)}=...$
Step 3. Combine numerators over the LCD
$= \displaystyle \frac{3(x-6)+4x}{x(x-6)} $
Step 4. Simplify, if possible.
$= \displaystyle \frac{3x-18+4x}{x(x-6)} $
= $\displaystyle \frac{7x-18}{x(x-6)}$
