Simplify $\frac{\sqrt{x^4 +3 x^2}}{x}$ The question states to simplify $$\frac{\sqrt{x^4 +3 x^2}}{x}$$where x is negative.

and part b is Let g(x) be the result from the simplification. Are f and g two equal functions? Y/N?

Much help is appreciated as i am struggling.
$\frac{\sqrt{x^{4}+3x^{2}}}{x}=\frac{\sqrt{x^{2}(x^{2}+3)}}{x}=\frac{|x|}{x}\sqrt{x^{2}+3}=\frac{-x}{x}\sqrt{x^{2}+3}=-\sqrt{x^{2}+3}$

$f(x)=\frac{\sqrt{x^{4}+3x^{2}}}{x}$ and $g(x)=-\sqrt{x^{2}+3}$ will agree as functions for all $x&lt;0$ but the formula for $f$ is not defined at $0$.
The answer is $\sqrt{x^2 + 3}$, and I don't know yet how to display so nicely...