Answer
$\displaystyle \frac{4x+8}{x^{2}}$
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: $\qquad x,x$
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
(one x is already in, we add the second x)
List = $x,x$
$LCD=x^{2}$
Step 2. Rewrite each expression with the LCD:
$\displaystyle \frac{4}{x}\cdot\frac{x}{x}+\frac{8}{x^{2}}=\frac{4x}{x^{2}}+\frac{8}{x^{2}}=...$
Step 3. Combine numerators over the LCD
$=\displaystyle \frac{4x+8}{x^{2}}$
Step 4. Simplify, if possible.
$=\displaystyle \frac{4(x+2)}{x^{2}} \qquad$... nothing to simplify.
