Answer
$-\displaystyle \frac{1}{y}$
Work Step by Step
To subtract rational expressions with the same denominator,
subtract numerators and place the difference over the common denominator.
If possible, factor and simplify the result.
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Don't forget to place the second numerator in parentheses when subtracting.
$\displaystyle \frac{3y^{2}-1}{3y^{3}}-\frac{6y^{2}-1}{3y^{3}}= \displaystyle \frac{3y^{2}-1-(6y^{2}-1)}{3y^{3}}$
$= \displaystyle \frac{3y^{2}-1-6y^{2}+1}{3y^{3}}$
$= \displaystyle \frac{-3y^{2}}{3y^{3}}$
$=\displaystyle \frac{3y^{2}(-1)}{3y^{2}(y)}$
... reduce (divide the numerator and denominator with common factors)
$=-\displaystyle \frac{1}{y}$
