Can I find the degree of an expression?

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Question: what is the degree of the following expression? $$\frac{x^2+1}{6x-2}$$

If the above question has a degree, please tell me the difference between the degree of a polynomial and the degree of an expression?

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By one definition of degree, the degree of a rational function is the difference in the degrees between the numerator and the denominator. Then the degree here is $1$. This means that as $|x|\to\infty$ this behaves like a multiple of $x$, specifically $\frac x6$.