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$\begin{array}{l} \lim \limits_{x\to -\frac{1}{3} }\frac{18x^{3}+21x^{2}+8x+1}{9x^{3}-3x^{2}-5x-1} \\ \text{Lopital}\\ \frac{\frac{d}{dx} \left( 18x^{3}\right) +\frac{d}{dx} \left( 21x^{2}\right) +\frac{d}{dx} \left( 8x\right) +\frac{d}{dx} (1)}{\frac{d}{dx} \left( 9x^{3}\right) -\frac{d}{dx} \left( 3x^{2}\right) -\frac{d}{dx} \left( 5x\right) -\frac{d}{dx} \left( 1\right) } \\ \lim \limits_{x\to -\frac{1}{3} }\left( \frac{54x^{2}+42x+8}{27x^{2}-6x-5} \right) \\ \text{Lopital}\\ \frac{\frac{d}{dx} (54x^{2})+\frac{d}{dx} (42x)+\frac{d}{dx} (8)}{\frac{d}{dx} (27x^{2}-\frac{d}{dx} (6x)-\frac{d}{dx} (5)} \\ \lim \limits_{x\to -\frac{1}{3} }\left( \frac{108x+42}{54x-6} \right) \\ \frac{-108\times \frac{1}{3} +42}{-54\times \frac{1}{3} -6} =\frac{42-36}{-18-6} =\frac{6}{-24} =-\frac{1}{4} \end{array}$