<s>[INST] How do you factor $3x^{3/2} -9x^{1/2}+6x^{-1/2}$? How do you factor $3x^{3/2} -9x^{1/2}+6x^{-1/2}$ ?
I factored out a 3 to get: 
$3(x^{3/2} -3x^{1/2}+2x^{-1/2})$, but it seems this can be factored further.
 [/INST] $$ 3 x^{\frac{3}{2}} -9 x^{\frac{1}{2}} + 6x^{-\frac{1}{2}}$$
Factor out $\sqrt{x}$ to get
$$\sqrt{x} (3 x - 9 + 6x^{-1})$$
Furthermore you get
$$\sqrt{x} 3(x - 3 + 2x^{-1})$$
and then
$$\sqrt{x} 3 \frac{(x-2)(x-1)}{x}$$
Simplify:
$$3 \frac{(x-2)(x-1)}{\sqrt{x}}$$
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