$$\lim_{n\to \infty}n^{3/2}(\sqrt{n+1}+\sqrt{n-1}-2\sqrt{n})$$
What I tried doing was multiplying by the reciprocal of the expression in parenthesis:
$=\lim_{n\to \infty}n^{3/2}\frac{(n+1+2\sqrt{n^2-1}+n-1)-4n}{\sqrt{n+1}+\sqrt{n-1}+2\sqrt{n}}=\lim_{n\to \infty}n^{3/2}\frac{2\sqrt{n^2-1}-2n}{\sqrt{n+1}+\sqrt{n-1}+2\sqrt{n}}=$
...
Ok, I just realized how to solve it but I'll post it in case it helps someone. I multiplied and divided by the numerator's reciprocal and get:
$=\lim_{n\to \infty}\frac{n^{3/2}(4n^2-4-4n^2)}{(2\sqrt{n^2-1}+2n)(\sqrt{n+1}+\sqrt{n-1}+2\sqrt{n})}=-\frac{1}{4}$