Question

vertical and horizontal asymptotes of x^2+2/3-x

Answer 1

Here, the vertical asymptote(s) will be where the function is not defined. Here the function is not defined where 3-x = 0.

Answer 2

Horizontal asymptotes follow simply:
1) Degree of numerator = degree of denominator: asymptote is y = coef of num / coef of den

2) Degree of numerator > degree of denominator: no asymptote

3) Degree of denominator > degree of numerator: asymptote is at y=0