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

$G (x) = \frac{x}{x^{2} - 4}$

Find the x-intercepts.

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

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

Set the numerator equal to zero.

$x = 0$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the denominator.

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

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

Subtract $4$ from $0$ .

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

Divide $0$ by $- 4$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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