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

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

Step 1

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

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$2 x + 2 = 0$

Solve the equation for $x$ .

Subtract $2$ from both sides of the equation.

$2 x = - 2$

Divide each term in $2 x = - 2$ by $2$ and simplify.

Divide each term in $2 x = - 2$ by $2$ .

$\frac{2 x}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2}{2}$

Divide $x$ by $1$ .

$x = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$x = - 1$

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

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

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