\begin{equation*}
\begin{split}
& \lim_{x \rightarrow 1} \: \frac{x^3 - 1}{x^5 - 1} \\\\
& \lim_{x \rightarrow 1} \: \frac{3x^2}{5x^4} \\\\
& \lim_{x \rightarrow 1} \: \frac{3 \cancel{x^2}}{5 \cancel{x^4}} \\\\
& \lim_{x \rightarrow 1} \: \frac{3}{5x^2} \\\\
& \frac{3}{5 \:.\: (1)^2} \\\\
& \frac 35
\end{split}
\end{equation*}
