Answer
$\displaystyle \frac{17}{(y-3)(y-4)} $
Work Step by Step
1. Find the LCD .
1st denominator = $(y-3)(x-4)$
2nd denominator = $(y-3)$
List factors of the 1st denominator.
From each next denominator, add only those factors that do not yet appear in the list.
LCD = $(y-3)(y-4)$
2. Rewrite each rational expression with the the LCDas the denominator
= $\displaystyle \frac{2y+9}{(y-3)(y-4)}-\frac{2(y-4)}{(y-3)(y-4)}$
3. Add or subtract numerators, placing the resulting expression over the LCD.
= $\displaystyle \frac{2y+9-2(y-4)}{(y-3)(y-4)}$
4. If possible, simplify.
= $\displaystyle \frac{2y+9-2y+8}{(y-3)(y-4)} $
= $\displaystyle \frac{17}{(y-3)(y-4)} $
