Question Number 184793 by Spillover last updated on 11/Jan/23
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}−\sqrt{{x}+\mathrm{2}}} \\ $$$$ \\ $$
Answered by MJS_new last updated on 11/Jan/23
$$=\frac{\left({x}^{\mathrm{2}} −\mathrm{4}\right)\left(\sqrt{\mathrm{3}{x}−\mathrm{2}}+\sqrt{{x}+\mathrm{2}}\right)}{\mathrm{2}\left({x}−\mathrm{2}\right)}=\frac{\left({x}+\mathrm{2}\right)\left(\sqrt{\mathrm{3}{x}−\mathrm{2}}+\sqrt{{x}+\mathrm{2}}\right)}{\mathrm{2}} \\ $$$$\mathrm{answer}\:\mathrm{is}\:\mathrm{8} \\ $$
Commented by Spillover last updated on 11/Jan/23
$${great} \\ $$