how would you simplify this

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

by dividing x^(1/2) and (1/(2x^(1/2))) from the equation?

\(\displaystyle \frac{\sqrt{x}(2x+4)-\frac{\left(x^2+4x+3\right)}{2\sqrt{x}}}{x}\)

\(\displaystyle =\frac{\frac{2\sqrt{x}\sqrt{x}(2x+4)-\left(x^2+4x+3\right)}{2\sqrt{x}}}{x}\)

\(\displaystyle =\frac{2\sqrt{x}\sqrt{x}(2x+4)-\left(x^2+4x+3\right)}{2x\sqrt{x}}\)

\(\displaystyle =\frac{2x(2x+4)-\left(x^2+4x+3\right)}{2x\sqrt{x}}\)

\(\displaystyle =\frac{4x^2+8x-x^2-4x-3}{2x\sqrt{x}}=\frac{3x^2+4x-3}{2x\sqrt{x}}\)

that's about simplest