Find the x and y Intercepts (4x)/(x^2-16)

$\frac{4 x}{x^{2} - 16}$

Step 1

Write $\frac{4 x}{x^{2} - 16}$ as an equation.

$y = \frac{4 x}{x^{2} - 16}$

Step 2

Find the x-intercepts.

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

$0 = \frac{4 x}{x^{2} - 16}$

Solve the equation.

Set the numerator equal to zero.

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

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 $y$ .

$y = \frac{4 (0)}{{(0)}^{2} - 16}$

Solve the equation.

Remove parentheses.

$y = \frac{4 (0)}{0^{2} - 16}$

Remove parentheses.

$y = \frac{4 (0)}{{(0)}^{2} - 16}$

Simplify $\frac{4 (0)}{{(0)}^{2} - 16}$ .

Multiply $4$ by $0$ .

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

Simplify the denominator.

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

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

Subtract $16$ from $0$ .

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

Divide $0$ by $- 16$ .

$y = 0$

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 (4x)/(x^2-16)

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