#### Answer

$\displaystyle \frac{2}{3y^{2}}$

#### Work Step by Step

To add rational expressions with the same denominator,
add numerators and place the sum over the common denominator.
If possible, factor and simplify the result.
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$\displaystyle \frac{y+2}{6y^{3}}+\frac{3y-2}{6y^{3}} = \displaystyle \frac{y+2+3y-2}{6y^{3}}$
$= \displaystyle \frac{4y}{6y^{3}}$
$= \displaystyle \frac{2y(2)}{2y(3y^{2})}\qquad$... reduce the common factors
$=\displaystyle \frac{2}{3y^{2}}$