Giải thích các bước giải:
$\begin{array}{l}
\mathop {\lim }\limits_{x \to 1} \dfrac{{\sqrt {8{x^3} - 23{x^2} + 28x - 4} - \sqrt[3]{{9{x^2} + 9x + 9}}}}{{{{\left( {x - 1} \right)}^3}}}\\
= \mathop {\lim }\limits_{x \to 1} \dfrac{{\left( {\sqrt {8{x^3} - 23{x^2} + 28x - 4} - \left( {x + 2} \right)} \right) + \left( {\left( {x + 2} \right) - \sqrt[3]{{9{x^2} + 9x + 9}}} \right)}}{{{{\left( {x - 1} \right)}^3}}}\\
= \mathop {\lim }\limits_{x \to 1} \dfrac{{\dfrac{{8{x^3} - 24{x^2} + 24x - 8}}{{\sqrt {8{x^3} - 23{x^2} + 28x - 4} + x + 2}}}}{{{{\left( {x - 1} \right)}^3}}} + \mathop {\lim }\limits_{x \to 1} \dfrac{{\dfrac{{{{\left( {x + 2} \right)}^3} - \left( {9{x^2} + 9x + 9} \right)}}{{{{\left( {x + 2} \right)}^2} + \left( {x + 2} \right)\sqrt[3]{{9{x^2} + 9x + 9}} + {{\left( {\sqrt[3]{{9{x^2} + 9x + 9}}} \right)}^2}}}}}{{{{\left( {x - 1} \right)}^3}}}\\
= \mathop {\lim }\limits_{x \to 1} \dfrac{{8{{\left( {x - 1} \right)}^3}}}{{{{\left( {x - 1} \right)}^3}\left( {\sqrt {8{x^3} - 23{x^2} + 28x - 4} + x + 2} \right)}} + \mathop {\lim }\limits_{x \to 1} \dfrac{{{x^3} - 3{x^2} + 3x - 1}}{{\left( {{{\left( {x + 2} \right)}^2} + \left( {x + 2} \right)\sqrt[3]{{9{x^2} + 9x + 9}} + {{\left( {\sqrt[3]{{9{x^2} + 9x + 9}}} \right)}^2}} \right){{\left( {x - 1} \right)}^3}}}\\
= \mathop {\lim }\limits_{x \to 1} \dfrac{8}{{\sqrt {8{x^3} - 23{x^2} + 28x - 4} + x + 2}} + \mathop {\lim }\limits_{x \to 1} \dfrac{1}{{{{\left( {x + 2} \right)}^2} + \left( {x + 2} \right)\sqrt[3]{{9{x^2} + 9x + 9}} + {{\left( {\sqrt[3]{{9{x^2} + 9x + 9}}} \right)}^2}}}\\
= \dfrac{8}{{\sqrt {8 - 23 + 28 - 4} + 1 + 2}} + \dfrac{1}{{{{\left( {1 + 2} \right)}^2} + \left( {1 + 2} \right)\sqrt[3]{{9 + 9 + 9}} + {{\left( {\sqrt[3]{{9 + 9 + 9}}} \right)}^2}}}\\
= \dfrac{{37}}{{27}}
\end{array}$
