The numerator has degree 1, and the denominator has degree 2. For large [tex]x[/tex], the denominator will dominate, so the limit would be 0.
Put another way, we have
[tex]\dfrac{2x+7}{x^2-x}=\dfrac{\frac2x+\frac7{x^2}}{1-\frac1x}[/tex]
and each fraction with [tex]x[/tex] will aproach 0. The numerator itself approaches 0 while the denominator approaches 1, so the overall limit is 0.
