Find the Vertical and Horizontal Intercept(s) f(x)=(x^2-1)/(x^2+4x-5)

$f (x) = \frac{x^{2} - 1}{x^{2} + 4 x - 5}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x^{2} - 1}{x^{2} + 4 x - 5}$

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 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.

$x = 1, - 1$

Exclude the solutions that do not make $0 = \frac{x^{2} - 1}{x^{2} + 4 x - 5}$ true.

$x = - 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 1}{{(0)}^{2} + 4 (0) - 5}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 1}{{(0)}^{2} + 4 (0) - 5}$

Remove parentheses.

$y = \frac{0^{2} - 1}{0^{2} + 4 (0) - 5}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 1}{{(0)}^{2} + 4 (0) - 5}$

Simplify $\frac{{(0)}^{2} - 1}{{(0)}^{2} + 4 (0) - 5}$ .

Simplify the numerator.

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

$y = \frac{0 - 1}{0^{2} + 4 (0) - 5}$

Subtract $1$ from $0$ .

$y = \frac{- 1}{0^{2} + 4 (0) - 5}$

Simplify the denominator.

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

$y = \frac{- 1}{0 + 4 (0) - 5}$

Multiply $4$ by $0$ .

$y = \frac{- 1}{0 + 0 - 5}$

Add $0$ and $0$ .

$y = \frac{- 1}{0 - 5}$

Subtract $5$ from $0$ .

$y = \frac{- 1}{- 5}$

Dividing two negative values results in a positive value.

$y = \frac{1}{5}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{5})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{1}{5})$

Step 4

Find the Vertical and Horizontal Intercept(s) f(x)=(x^2-1)/(x^2+4x-5)

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