tolong di jawab beserta caranya

[tex]\lim_ {x\rightarrow2} \frac{\sqrt{2x}-2}{\sqrt{3x-2}-\sqrt{x+2}}[/tex]
[tex]=\lim_ {x\rightarrow2} \frac{(2x)^{\frac12}-2}{(3x-2)^{\frac12}-(x+2)^{\frac12}}[/tex]
kita pakai turunan
[tex]=\lim_ {x\rightarrow2} \frac{\frac22(2x)^{-\frac12}-0}{\frac32(3x-2)^{-\frac12}-\frac12(x+2)^{-\frac12}}[/tex]
[tex]=\lim_ {x\rightarrow2} \frac{\frac1{\sqrt{2x}}}{\frac3{2\sqrt{3x-2}}-\frac1{2\sqrt{x+2}}}[/tex]
[tex]=\frac{\frac1{\sqrt{4}}}{\frac3{2\sqrt{6-2}}-\frac1{2\sqrt{2+2}}}[/tex]
[tex]=\frac{\frac1{\sqrt{4}}}{\frac3{2\sqrt{4}}-\frac1{2\sqrt{4}}}[/tex]
[tex]=\frac{\frac12}{\frac3{2.2}-\frac1{2.2}}[/tex]
[tex]=\frac{\frac12}{\frac3{4}-\frac1{4}}[/tex]
[tex]=\frac{\frac12}{\frac24}[/tex]
[tex]=\frac{\frac12}{\frac12}[/tex]
[tex]={\frac12}\times{\frac21}[/tex]
[tex]=1[/tex]

semoga membantu, mohon dikoreksi bila ada kesalahan