\[\begin{split} &\lim_{n \to \infty} \frac{2x^2-1}{7x^2+2x}=\\[16pt] &=\lim_{n \to \infty} \frac{2x^2-1}{7x^2+2x}\cdot \frac{\frac{1}{x^2}}{\frac{1}{x^2}}=\\[16pt] &=\lim_{n \to \infty} \frac{2-\dfrac{1}{x^2}}{7+\dfrac{2}{x}}=\\[16pt] &=\frac{2}{7} \end{split}\]