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[tex] \lim_{x \to\ {3 } \, \frac{ \sqrt{2x-2}-2}{ \sqrt{3x} - 3 } [/tex]

[tex]\lim_{x \to\ {3 } \, \frac{ \sqrt{2x-2}-2}{ \sqrt{3x} - 3 }\, \frac{ \sqrt{3x}+3}{ \sqrt{3x}+3 }\, \frac{ \sqrt{2x-2}+2}{ \sqrt{2x-2}+2 } [/tex]

[tex] \lim_{x \to \ 3} \frac{(2x-6)( \sqrt{3x} +3) }{ (3x-9)( \sqrt{2x}\,+2) } [/tex]

[tex]\lim_{x \to \ 3} \frac{2(x-3)( \sqrt{3x} +3) }{ 3(x-3)( \sqrt{2x}\,+2) } [/tex]

[tex]\lim_{x \to \ 3} \frac{2( \sqrt{3x} +3) }{ 3( \sqrt{2x}\,+2) }\,= \frac{2 (3+3)}{3(2+2)}\,=\,1 [/tex]