Find the x and y Intercepts y=(3x)/(x^2+9)

$y = \frac{3 x}{x^{2} + 9}$

Find the x-intercepts.

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

$0 = \frac{3 x}{x^{2} + 9}$

Solve the equation.

Set the numerator equal to zero.

$3 x = 0$

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

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 $y$ .

$y = \frac{3 (0)}{{(0)}^{2} + 9}$

Solve the equation.

Remove parentheses.

$y = \frac{3 (0)}{0^{2} + 9}$

Remove parentheses.

$y = \frac{3 (0)}{{(0)}^{2} + 9}$

Simplify $\frac{3 (0)}{{(0)}^{2} + 9}$ .

Multiply $3$ by $0$ .

$y = \frac{0}{0^{2} + 9}$

Simplify the denominator.

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

$y = \frac{0}{0 + 9}$

Add $0$ and $9$ .

$y = \frac{0}{9}$

Divide $0$ by $9$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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