Because the degree in the numerator is 1 higher than that of the denominator, we have an oblique asymptote that is found by dividing the polynomials using long division. It's also possible and easier to use synthetic division. Put your 2 from x - 2 = 0 outside the "box" and the coefficients from the quadratic inside: 2 (-3 7 1). Bring down that -3 and multiply by the 2 to get -6. Put that -6 up under the 7 and add to get a 1. Multiply that 1 by the 2 to get 2. Put that 2 up under the 1 and add to get 3. That's your remainder...3. The -3 and the 1 are now the coefficients for the new polynomial that is one degree less than the degree of the polynomial we started with, called the depressed polynomial. It is -3x + 1. That's the equation of your oblique asymptote, then.
