Find the Roots (Zeros) (-x^2+1)/((x^2+1)^2)

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

Step 1

Set $\frac{- x^{2} + 1}{{(x^{2} + 1)}^{2}}$ equal to $0$ .

$\frac{- x^{2} + 1}{{(x^{2} + 1)}^{2}} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$- x^{2} + 1 = 0$

Solve the equation for $x$ .

Subtract $1$ from both sides of the equation.

$- x^{2} = - 1$

Divide each term in $- x^{2} = - 1$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 1$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 1}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 1}{- 1}$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x^{2} = 1$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Step 3