`~rai~`
\(\lim\limits_{x\to 2}\dfrac{\sqrt{3x-2}-\sqrt{x+2}}{\sqrt[3]{3x+2}-2}\\=\lim\limits_{x\to 2}\dfrac{(\sqrt{3x-2}-\sqrt{x+2})(\sqrt{3x-2}+\sqrt{x+2})(\sqrt[3]{3x+2}^2+2\sqrt[3]{3x-2}+4)}{(\sqrt[3]{3x+2}-2)(\sqrt[3]{3x+2}^2+2\sqrt[3]{3x+2}+4)(\sqrt{3x-2}+\sqrt{x+2})}\\=\lim\limits_{x\to 2}\dfrac{(3x-2-x-2)(\sqrt[3]{3x+2}^2+2\sqrt[3]{3x+2}+4)}{(3x+2-2^3)(\sqrt{3x-2}+\sqrt{x+2})}\\=\lim\limits_{x\to 2}\dfrac{2(x-2)(\sqrt[3]{3x+2}^2+2\sqrt[3]{3x+2}+4)}{3(x-2)(\sqrt{3x-2}+\sqrt{x+2})}\\=\lim\limits_{x\to 2}\dfrac{2(\sqrt[3]{3x+2}^2+2\sqrt[3]{3x+2}+4)}{3(\sqrt{3x-2}+\sqrt{x+2})}\\=\dfrac{2.(\sqrt[3]{3.2+2}^2+2\sqrt[3]{3.2+2}+4)}{3(\sqrt{3.2-2}+\sqrt{2+2})}\\=2.\)
