Do all functions with vertical asymptotes also have oblique asymptotes?

I just started learning about asymptotes in my Advanced Functions class, and as I was taking a look at all this stuff, a question came up. Do all rational functions that have vertical asymptotes also have an oblique asymptote? Or is an oblique asymptote only formed when the degree of the numerator is 1 higher than the degree of the denominator, and so only functions with a vertical asymptote with a degree of 1 can also have an oblique asymptote?

I just started learning about asymptotes in my Advanced Functions class, and as I was taking a look at all this stuff, a question came up. Do all rational functions that have vertical asymptotes also have an oblique asymptote? Or is an oblique asymptote only formed when the degree of the numerator is 1 higher than the degree of the denominator, and so only functions with a vertical asymptote with a degree of 1 can also have an oblique asymptote?