Find the x and y Intercepts y=(x^2-1)/(x^2-4)

$y = \frac{x^{2} - 1}{x^{2} - 4}$

Find the x-intercepts.

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

$0 = \frac{x^{2} - 1}{x^{2} - 4}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 1 = 0$

Solve the equation for $x$ .

Add $1$ to both sides of the equation.

$x^{2} = 1$

Take the square 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.

$x = 1, - 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 1, 0)$

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 1}{{(0)}^{2} - 4}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 1}{{(0)}^{2} - 4}$

Remove parentheses.

$y = \frac{0^{2} - 1}{0^{2} - 4}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 1}{{(0)}^{2} - 4}$

Simplify $\frac{{(0)}^{2} - 1}{{(0)}^{2} - 4}$ .

Simplify the numerator.

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

$y = \frac{0 - 1}{0^{2} - 4}$

Subtract $1$ from $0$ .

$y = \frac{- 1}{0^{2} - 4}$

Simplify the denominator.

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

$y = \frac{- 1}{0 - 4}$

Subtract $4$ from $0$ .

$y = \frac{- 1}{- 4}$

Dividing two negative values results in a positive value.

$y = \frac{1}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{4})$

List the intersections.

x-intercept(s): $(1, 0), (- 1, 0)$

y-intercept(s): $(0, \frac{1}{4})$

Find the x and y Intercepts y=(x^2-1)/(x^2-4)

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