Question

Solve:%7D" id="TexFormula1" title="\underset{x\rightarrow~3}{\lim}~\dfrac{2x^2-18}{x^2-3x}" alt="\underset{x\rightarrow~3}{\lim}~\dfrac{2x^2-18}{x^2-3x}" align="absmiddle" class="latex-formula">
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Answer 1

Hello, please consider the following.

$\displaystyle \lim_{x\rightarrow3}~\dfrac{2x^2-18}{x^2-3x} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x^2-3^2)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x-3)(x+3)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x+3)}{x} \\ \\ \\=\dfrac{2(3+3)}{3}\\ \\ \\=\dfrac{2*3*2}{3} =\Large \boxed{\sf \bf \ 4 \ }$

Thank you