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$L=\mathop {\lim }\limits_{x \to 2}\dfrac{\sqrt[3]{8x+11}-\sqrt{x+7}}{x^2-3x+2}$
$L=\mathop {\lim }\limits_{x \to 2}\dfrac{\sqrt[3]{8x+11}-3}{x^2-3x+2}-\mathop {\lim }\limits_{x \to 2}\dfrac{\sqrt{x+7}-3}{x^2-3x+2}$
$L=\mathop {\lim }\limits_{x \to
2}\dfrac{8}{(x-1)\left ( \sqrt[3]{(8x+11)^2}+3\sqrt[3]{8x+11}+9 \right )}-\mathop {\lim }\limits_{x \to
2}\dfrac{1}{(x-1)(\sqrt{x+7}+3)}$
$L=\dfrac{8}{9+9+9}-\dfrac{1}{6}=\dfrac{7}{54}$
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