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

$f (X) = \frac{x}{x^{2} - 1}$

Step 1

Find the x-intercepts.

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

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

Set the numerator equal to zero.

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the denominator.

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

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

Subtract $1$ from $0$ .

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

Divide $0$ by $- 1$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4