Answer
$\displaystyle \frac{3x+11}{4}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad 2$
List of factors of the second denominator: $\qquad 2,2$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $
List$=2,...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
(a 2 is added to the list)
List = $2,2, $
$LCD=4$
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{x+3}{2}\cdot\frac{2}{2}+\frac{x+5}{4}= \displaystyle \frac{2(x+3)}{4}+\frac{x+5}{4}=...$
Step 3. Combine numerators over the LCD
$= \displaystyle \frac{2(x+3)+x+5}{4} $
Step 4. Simplify, if possible.
$= \displaystyle \frac{2x+6+x+5}{4} $
= $\displaystyle \frac{3x+11}{4}$
