Find the x and y Intercepts (x^2-16)/(x+1)

$\frac{x^{2} - 16}{x + 1}$

Step 1

Write $\frac{x^{2} - 16}{x + 1}$ as an equation.

$y = \frac{x^{2} - 16}{x + 1}$

Step 2

Find the x-intercepts.

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

$0 = \frac{x^{2} - 16}{x + 1}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} - 16 = 0$

Solve the equation for $x$ .

Add $16$ to both sides of the equation.

$x^{2} = 16$

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

$x = \pm \sqrt{16}$

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (- 4, 0)$

Step 3

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} - 16}{(0) + 1}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 16}{(0) + 1}$

Remove parentheses.

$y = \frac{0^{2} - 16}{0 + 1}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 16}{(0) + 1}$

Simplify $\frac{{(0)}^{2} - 16}{(0) + 1}$ .

Simplify the numerator.

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

$y = \frac{0 - 16}{0 + 1}$

Subtract $16$ from $0$ .

$y = \frac{- 16}{0 + 1}$

Simplify the expression.

Add $0$ and $1$ .

$y = \frac{- 16}{1}$

Divide $- 16$ by $1$ .

$y = - 16$

y-intercept(s) in point form.

y-intercept(s): $(0, - 16)$

Step 4

List the intersections.

x-intercept(s): $(4, 0), (- 4, 0)$

y-intercept(s): $(0, - 16)$

Step 5

Find the x and y Intercepts (x^2-16)/(x+1)

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