## Precalculus: Mathematics for Calculus, 7th Edition

$3x^{-1/2}+4x^{1/2}+x^{3/2}=\dfrac{1}{\sqrt{x}}(x+3)(x+1)$
$3x^{-1/2}+4x^{1/2}+x^{3/2}$ 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: $...=\dfrac{1}{\sqrt{x}}(x+3)(x+1)$