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