deletions | additions       diff --git a/ratio.tex b/ratio.tex  index 5e34f2e..7fef363 100644  --- a/ratio.tex  +++ b/ratio.tex 
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\:&=\:\lim_{n\to\infty}\left|\:\frac{9}{(n\:+\:2)}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)}{4}\:\right| \\[1em]  \:&=\:\lim_{n\to\infty}\left|\:\frac{9(n\:+\:1)}{4(n\:+\:2)}\:\right| \\[1em]  \:&=\:\lim_{n\to\infty}\left|\:\frac{9n\left(\frac{n}{n}\:+\:\frac{1}{n}\right)}{4n\left(\frac{n}{n}\:+\:\frac{2}{n}\right)}\:\right| \\[1em]  \:&=\:\lim_{n\to\infty}\left|\:\frac{9\left(1\:+\:\frac{1}{n}\right)}{4\left(1\:+\:\frac{2}{n}\right)}\:\right| \\[1em]  \end{align}  \end{document}