## Thomas' Calculus 13th Edition

$$y=2 x .$$
Since the highest power of $x$ in the numerator is 1 more than the highest power of $x$ in the denominator, there is an oblique asymptote. $$y=\frac{2 x^{3 / 2}+2 x-3}{\sqrt{x}+1}=2 x-\frac{3}{\sqrt{x}+1},$$ Thus the oblique asymptote is $$y=2 x$$