Find the Roots (Zeros) y=(x^2-25)/(x^2+5x+5)

$y = \frac{x^{2} - 25}{x^{2} + 5 x + 5}$

Step 1

Set $\frac{x^{2} - 25}{x^{2} + 5 x + 5}$ equal to $0$ .

$\frac{x^{2} - 25}{x^{2} + 5 x + 5} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$x^{2} - 25 = 0$

Solve the equation for $x$ .

Add $25$ to both sides of the equation.

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$

Step 3