I have $3x^{-1/2} (x^2-3x+2)$ However, I just tried to expand, and the answer is not the same as the original question.
With fractional exponents I take out the smallest exponent, then I add the smallest exponents to those left in the non-factored equation. However, it does not seem to be working. Any ideas?
Best Answer
My answer is $3x^{-\frac{1}{2}}(x-1)(x-2)$:
$3x^{\frac{3}{2}}-9x^{1/2}+6x^{-\frac{1}{2}} = 3x^{\frac{1}{2}}(x-3+\frac{2}{x}) =3x^{\frac{1}{2}}(\frac{x^2-3x+2}{x})= 3x^{-\frac{1}{2}}(x^2-3x+2) = 3x^{-\frac{1}{2}}(x^2 -2x +1 - x +1) = 3x^{-\frac{1}{2}}((x-1)^2-(x-1)) = 3x^{-\frac{1}{2}}(x-1)(x-1-1) = 3x^{-\frac{1}{2}}(x-1)(x-2)$