Find the x and y Intercepts R(x)=3/(x^2-4)

$R (x) = \frac{3}{x^{2} - 4}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3}{x^{2} - 4}$

Solve the equation.

Set the numerator equal to zero.

$3 = 0$

Since $3 \neq 0$ , there are no solutions.

No solution

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = \frac{3}{{(0)}^{2} - 4}$

Solve the equation.

Remove parentheses.

$y = \frac{3}{0^{2} - 4}$

Remove parentheses.

$y = \frac{3}{{(0)}^{2} - 4}$

Simplify $\frac{3}{{(0)}^{2} - 4}$ .

Simplify the denominator.

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

$y = \frac{3}{0 - 4}$

Subtract $4$ from $0$ .

$y = \frac{3}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{3}{4}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{4})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{3}{4})$

Step 4