$lim_{xto 2}((sqrt(3x-2)-sqrt(x+2))/(sqrt(x^2-3x+2)))$ - Studentville

$lim_{xto 2}((sqrt(3x-2)-sqrt(x+2))/(sqrt(x^2-3x+2)))$

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Limite in forma indeterminata $frac{0}{0}$

$lim_{x rightarrow 2} frac{sqrt{3x-2}-sqrt{x+2}}{sqrt{x^2-3x+2}} =lim_{x rightarrow 2} frac{(sqrt{3x-2}-sqrt{x+2})(sqrt{3x-2}+sqrt{x+2})}{sqrt{x^2-3x+2} (sqrt{3x-2}+sqrt{x+2})} =$$lim_{x rightarrow 2} frac{3x-2-x-2}{sqrt{x-2} sqrt{x-1} (sqrt{3x-2}+sqrt{x+2})} = lim_{x rightarrow 2} frac{2 sqrt{x-2}}{sqrt{x-1} (sqrt{3x-2}+sqrt{x+2})} = 0$

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