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Question Number 184793 by Spillover last updated on 11/Jan/23

Evaluate   lim_(x→2)   ((x^2 −4)/( (√(3x−2))−(√(x+2))))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}−\sqrt{{x}+\mathrm{2}}} \\ $$$$ \\ $$

Answered by MJS_new last updated on 11/Jan/23

=(((x^2 −4)((√(3x−2))+(√(x+2))))/(2(x−2)))=(((x+2)((√(3x−2))+(√(x+2))))/2)  answer is 8

$$=\frac{\left({x}^{\mathrm{2}} −\mathrm{4}\right)\left(\sqrt{\mathrm{3}{x}−\mathrm{2}}+\sqrt{{x}+\mathrm{2}}\right)}{\mathrm{2}\left({x}−\mathrm{2}\right)}=\frac{\left({x}+\mathrm{2}\right)\left(\sqrt{\mathrm{3}{x}−\mathrm{2}}+\sqrt{{x}+\mathrm{2}}\right)}{\mathrm{2}} \\ $$$$\mathrm{answer}\:\mathrm{is}\:\mathrm{8} \\ $$

Commented by Spillover last updated on 11/Jan/23

great

$${great} \\ $$

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