Evaluate the Function f(-x)=(-x)/(-x^2+1)

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

Step 1

Simplify the denominator.

Rewrite $1$ as $1^{2}$ .

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

Reorder $- x^{2}$ and $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

$f (- x) = \frac{- x}{(1 + x) (1 - x)}$

Step 2

Move the negative in front of the fraction.

$f (- x) = - \frac{x}{(1 + x) (1 - x)}$

Step 3