Simplify (-x^2+1)/((x^2+1)^2)

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

Step 1

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

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

Step 2

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

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

Step 3

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 $b = x$ .

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