Answer
$$-7$$
Work Step by Step
We evaluate the limit:
\begin{aligned}
\lim_{y\to 1/3}\frac{3 y^{2}+5 y-2}{6 y^{2}-5 y+1} &=\lim_{y\to 1/3}\frac{3 y^{2}-y+6 y-2}{6 y^{2}-2 y-3 y+1} \\
&=\lim_{y\to 1/3}\frac{y(3 y-1)+2(3 y-1)}{2 y(3 y-1)-(3 y-1)} \\
&=\lim_{y\to 1/3}\frac{(3 y-1)(y+2)}{(3 y-1)(2 y-1)}\\
&=\lim_{y\to 1/3}\frac{y+2}{2 y-1}\\
&= \frac{7/3}{-1/3}=-7
\end{aligned}
