Answer
$\displaystyle \frac{11y+2}{3y(y+1)}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad (y+1)$
List of factors of the second denominator: $\qquad 3,y$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $
List$= (y+1),...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
($3$ and $y$ are added to the list)
List = $(y+1),3,y$
$LCD=3y(y+1)$
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{3}{y+1}\cdot\frac{3y}{3y}+\frac{2}{3y}\cdot\frac{(y+1)}{(y+1)}= \frac{3(3y)}{3y(y+1)} +\frac{2(y+1)}{3y(y+1)}=...$
Step 3. Combine numerators over the LCD
$=$ $ \displaystyle \frac{3(3y)+2(y+1)}{3y(y+1)} $
Step 4. Simplify, if possible.
$= \displaystyle \frac{9y+2y+2}{3y(y+1)}$
= $\displaystyle \frac{11y+2}{3y(y+1)}$
