Find the x and y Intercepts f(x)=(5x^2)/(2x^2+3x)

$f (x) = \frac{5 x^{2}}{2 x^{2} + 3 x}$

Find the x-intercepts.

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

$0 = \frac{5 x^{2}}{2 x^{2} + 3 x}$

Solve the equation.

Set the numerator equal to zero.

$5 x^{2} = 0$

Solve the equation for $x$ .

Divide each term in $5 x^{2} = 0$ by $5$ and simplify.

Divide each term in $5 x^{2} = 0$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{0}{5}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Exclude the solutions that do not make $0 = \frac{5 x^{2}}{2 x^{2} + 3 x}$ true.

$No solution$

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = \frac{5 {(0)}^{2}}{2 {(0)}^{2} + 3 (0)}$

The equation has an undefined fraction.

Undefined

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

y-intercept(s): $None$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$