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

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

Step 1

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

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

Step 2

Simplify the left side.

Cancel the common factor of $x + h$ .

Cancel the common factor.

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

Divide $f$ by $1$ .

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

Step 3

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

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

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