Precalculus: Mathematics for Calculus, 7th Edition

$x^{-3/2}+2x^{-1/2}+x^{1/2}=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$
$x^{-3/2}+2x^{-1/2}+x^{1/2}$ 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: $...=\dfrac{1}{\sqrt{x^{3}}}(x+1)^{2}$