Analyze what value a rational function approaches at infinity (if at all).

Problem

Let f, left parenthesis, x, right parenthesis, equals, start fraction, minus, 6, x, start superscript, 2, end superscript, plus, x, minus, 1, divided by, x, start superscript, 2, end superscript, plus, 3, end fraction.
Find limxf(x)\displaystyle\lim_{x\to\infty}f(x).
Please choose from one of the following options.