Evaluate f(3x)=x/(x^2+1)

$f (3 x) = \frac{x}{x^{2} + 1}$

Remove parentheses.

$f \cdot 3 x = \frac{x}{x^{2} + 1}$

Divide each term in $(f \cdot (3 x)) = \frac{x}{x^{2} + 1}$ by $3 x$ and simplify.

Divide each term in $(f \cdot (3 x)) = \frac{x}{x^{2} + 1}$ by $3 x$ .

$\frac{(f \cdot (3 x))}{3 x} = \frac{\frac{x}{x^{2} + 1}}{3 x}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{f \cdot 3 x}{3 x} = \frac{\frac{x}{x^{2} + 1}}{3 x}$

Rewrite the expression.

$\frac{f x}{x} = \frac{\frac{x}{x^{2} + 1}}{3 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{f x}{x} = \frac{\frac{x}{x^{2} + 1}}{3 x}$

Divide $f$ by $1$ .

$f = \frac{\frac{x}{x^{2} + 1}}{3 x}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{x}{x^{2} + 1} \cdot \frac{1}{3 x}$

Cancel the common factor of $x$ .

Factor $x$ out of $3 x$ .

$f = \frac{x}{x^{2} + 1} \cdot \frac{1}{x \cdot 3}$

Cancel the common factor.

$f = \frac{x}{x^{2} + 1} \cdot \frac{1}{x \cdot 3}$

Rewrite the expression.

$f = \frac{1}{x^{2} + 1} \cdot \frac{1}{3}$

Multiply $\frac{1}{x^{2} + 1}$ by $\frac{1}{3}$ .

$f = \frac{1}{(x^{2} + 1) \cdot 3}$

Move $3$ to the left of $x^{2} + 1$ .

$f = \frac{1}{3 (x^{2} + 1)}$