[tex]\bf \lim\limits_{x\to 6}~\cfrac{x^2+x+42}{x-6}\implies \lim\limits_{x\to 6}~\cfrac{(x+7)(x-6)}{(x-6)}\implies \lim\limits_{x\to 6}~x+7
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\lim\limits_{x\to 6}~(6)+7=13
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\textit{since the original equation holds for all, }x\ne 6,\textit{ then it approaches}\\
\textit{the same limit as }x+7[/tex]
