Answer
$\displaystyle \frac{x+1}{2}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad 2.3$
List of factors of the second denominator: $\qquad 3$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $
List$=2,3,...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
(none are added to the list)
List = $2,3, $
$LCD=$6
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{x-1}{6}+\frac{x+2}{3}\cdot\frac{2}{2}= \displaystyle \frac{x-1}{6}+\frac{2(x+2)}{6}=...$
Step 3. Combine numerators over the LCD
$= \displaystyle \frac{x-1+2(x+2)}{6} $
Step 4. Simplify, if possible.
$= \displaystyle \frac{x-1+2x+4}{6} $
$= \displaystyle \frac{3x+3}{6} $
$= \displaystyle \frac{3(x+1)}{6} \qquad$ ... reduce by the common factor,3
= $\displaystyle \frac{x+1}{2}$