Evaluate f(r^2)=x/(|x|)

$f (r^{2}) = \frac{x}{| x |}$

Divide each term in $f r^{2} = \frac{x}{| x |}$ by $r^{2}$ .

$\frac{f r^{2}}{r^{2}} = \frac{\frac{x}{| x |}}{r^{2}}$

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{f r^{2}}{r^{2}} = \frac{\frac{x}{| x |}}{r^{2}}$

Divide $f$ by $1$ .

$f = \frac{\frac{x}{| x |}}{r^{2}}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{x}{| x |} \cdot \frac{1}{r^{2}}$

Combine.

$f = \frac{x \cdot 1}{| x | r^{2}}$

Simplify the expression.

Multiply $x$ by $1$ .

$f = \frac{x}{| x | r^{2}}$

Reorder factors in $\frac{x}{| x | r^{2}}$ .

$f = \frac{x}{r^{2} | x |}$