Find the x and y Intercepts (8x)/(x^2-4)

$\frac{8 x}{x^{2} - 4}$

Step 1

Write $\frac{8 x}{x^{2} - 4}$ as an equation.

$y = \frac{8 x}{x^{2} - 4}$

Step 2

Find the x-intercepts.

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

$0 = \frac{8 x}{x^{2} - 4}$

Solve the equation.

Set the numerator equal to zero.

$8 x = 0$

Divide each term in $8 x = 0$ by $8$ and simplify.

Divide each term in $8 x = 0$ by $8$ .

$\frac{8 x}{8} = \frac{0}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{0}{8}$

Divide $x$ by $1$ .

$x = \frac{0}{8}$

Simplify the right side.

Divide $0$ by $8$ .

$x = 0$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = \frac{8 (0)}{{(0)}^{2} - 4}$

Solve the equation.

Remove parentheses.

$y = \frac{8 (0)}{0^{2} - 4}$

Remove parentheses.

$y = \frac{8 (0)}{{(0)}^{2} - 4}$

Simplify $\frac{8 (0)}{{(0)}^{2} - 4}$ .

Multiply $8$ by $0$ .

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

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): $(0, 0)$

Step 4

List the intersections.

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

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

Step 5

Find the x and y Intercepts (8x)/(x^2-4)

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