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

$\frac{4 x}{x^{3} + 2 x^{2} - 3 x}$

Step 1

Write $\frac{4 x}{x^{3} + 2 x^{2} - 3 x}$ as an equation.

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

Step 2

Find the x-intercepts.

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

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

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 $4$ .

$x = 0$

Exclude the solutions that do not make $0 = \frac{4 x}{x^{3} + 2 x^{2} - 3 x}$ true.

$No solution$

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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

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

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): $None$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$

Step 5