Answer
$\displaystyle \frac{11y+15}{4y(y+5)}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad (y+5)$
List of factors of the second denominator: $\qquad 2,2,y$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $
List$= (y+5),...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
($2,2,$ and $y$ are added to the list)
List = $(y+5),2,2,y$
$LCD=4y(y+5)$
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{2}{y+5}\cdot\frac{4y}{4y}+\frac{3}{4y}\cdot\frac{(y+5)}{(y+5)}= \frac{2(4y)}{4y(y+5)} +\frac{3(y+5)}{4y(y+5)}=...$
Step 3. Combine numerators over the LCD
$=$ $\displaystyle \frac{2(4y)+3(y+5)}{4y(y+5)}$
Step 4. Simplify, if possible.
$= \displaystyle \frac{8y+3y+15}{4y(y+5)}$
= $\displaystyle \frac{11y+15}{4y(y+5)}$
