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