Question

Find the limit of the function algebraically x-->9 x^2-81/x-9

Answer 1

$\bf \lim\limits_{x\to 9}~\cfrac{x^2-81}{x-9}\implies \cfrac{\stackrel{\textit{difference of squares}}{x^2-9^2}}{x-9}\implies \cfrac{\underline{(x-9)}(x+9)}{\underline{x-9}}\implies x+9 \\\\\\ \lim\limits_{x\to 9}~x+9\implies 9+9\implies 18$