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DETAILS SCALC9 3.4.007.MI.
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Evaluate the limit using the appropriate properties of limits. (If the limit is infinite, enter ' $\infty$ ' or '- $\infty$ ', as appropriate. If the limit does not otherwise exist, enter DNE.)
\[
\lim _{x \rightarrow \infty} \frac{6 x^{2}-5}{7 x^{2}+x-3}
\]
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Final Answer: $\boxed{\frac{6}{7}}$

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Step 1 ：The limit is a ratio of two polynomials of the same degree. In such cases, the limit as x approaches infinity is the ratio of the leading coefficients. In this case, the leading coefficients are 6 and 7. Therefore, the limit should be $\frac{6}{7}$.

Step 2 ：Final Answer: $\boxed{\frac{6}{7}}$

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