Answer
$\displaystyle \frac{7x-20}{x(x-5)}$
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: $\qquad (x-5)$
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
($(x-5)$ is added to the list)
List = $x,(x-5), $
$LCD=x(x-5)$
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{4}{x}\cdot\frac{(x-5)}{(x-5)}+\frac{3}{(x-5)}\cdot\frac{x}{x}= \displaystyle \frac{4(x-5)}{x(x-5)}+\frac{3x}{x(x-5)}=...$
Step 3. Combine numerators over the LCD
$= \displaystyle \frac{4(x-5)+3x}{x(x-5)} $
Step 4. Simplify, if possible.
$= \displaystyle \frac{4x-20+3x}{x(x-5)} $
= $\displaystyle \frac{7x-20}{x(x-5)}$