Factor 3x^(-1/2)+4x^(1/2)+x^(3/2)

$3 x^{- \frac{1}{2}} + 4 x^{\frac{1}{2}} + x^{\frac{3}{2}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 \frac{1}{x^{\frac{1}{2}}} + 4 x^{\frac{1}{2}} + x^{\frac{3}{2}}$

Combine $3$ and $\frac{1}{x^{\frac{1}{2}}}$ .

$\frac{3}{x^{\frac{1}{2}}} + 4 x^{\frac{1}{2}} + x^{\frac{3}{2}}$

Reorder terms.

$4 x^{\frac{1}{2}} + x^{\frac{3}{2}} + \frac{3}{x^{\frac{1}{2}}}$