Answer
$x^{-1/2}(x+1)(5x-3)$ or $\dfrac{(x+1)(5x-3)}{x^{1/2}}$ or $\dfrac{(x+1)(5x-3)}{\sqrt{x}}$
Work Step by Step
$-3x^{-1/2}+2x^{1/2}+5x^{3/2}$
Take out common factor $x^{-1/2}$:
$-3x^{-1/2}+2x^{1/2}+5x^{3/2}=x^{-1/2}(-3+2x+5x^{2})=...$
Rearrange the expression inside the parentheses:
$...=x^{-1/2}(5x^{2}+2x-3)=...$
Factor the parentheses:
$...=x^{-1/2}(x+1)(5x-3)$