Answer
$=2, \displaystyle \quad x\neq-\frac{5}{6}$
Work Step by Step
The fractions have a common denominator, we add the numerators...
$\displaystyle \frac{4x+1}{6x+5}+\frac{8x+9}{6x+5}=\frac{4x+1+8x+9}{6x+5}$
$=\displaystyle \frac{12x+10}{6x+5}$
... factor what we can...
$=\displaystyle \frac{2(6x+5)}{(6x+5)}$
... exclude values that yield 0 in the denominator:
$x\displaystyle \neq-\frac{5}{6}$
... and, cancel common factors
$=2, \displaystyle \quad x\neq-\frac{5}{6}$
