Find the x and y Intercepts y=(x^2-4)/(x^2-9)

$y = \frac{x^{2} - 4}{x^{2} - 9}$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{x^{2} - 4}{x^{2} - 9}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 4 = 0$

Solve the equation for $x$ .

Add $4$ to both sides of the equation.

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

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

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 2, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{{(0)}^{2} - 4}{{(0)}^{2} - 9}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 4}{{(0)}^{2} - 9}$

Remove parentheses.

$y = \frac{0^{2} - 4}{0^{2} - 9}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 4}{{(0)}^{2} - 9}$

Simplify $\frac{{(0)}^{2} - 4}{{(0)}^{2} - 9}$ .

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 - 4}{0^{2} - 9}$

Subtract $4$ from $0$ .

$y = \frac{- 4}{0^{2} - 9}$

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{- 4}{0 - 9}$

Subtract $9$ from $0$ .

$y = \frac{- 4}{- 9}$

Dividing two negative values results in a positive value.

$y = \frac{4}{9}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{4}{9})$

List the intersections.

x-intercept(s): $(2, 0), (- 2, 0)$

y-intercept(s): $(0, \frac{4}{9})$

Find the x and y Intercepts y=(x^2-4)/(x^2-9)

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