Answer
$x^{-3/2}+2x^{-1/2}+x^{1/2}=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$
Work Step by Step
$x^{-3/2}+2x^{-1/2}+x^{1/2}$
Take out common factor $x^{-3/2}$:
$x^{-3/2}+2x^{-1/2}+x^{1/2}=x^{-3/2}(1+2x+x^{4/2})=...$
$...=\dfrac{1}{\sqrt{x^{3}}}(x^{2}+2x+1)=...$
Factor the expression inside the parentheses, which is a perfect square trinomial:
$...=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$
