Find the x and y Intercepts (4x+8)/(x^2+2x)

$\frac{4 x + 8}{x^{2} + 2 x}$

Step 1

Write $\frac{4 x + 8}{x^{2} + 2 x}$ as an equation.

$y = \frac{4 x + 8}{x^{2} + 2 x}$

Step 2

Find the x-intercepts.

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

$0 = \frac{4 x + 8}{x^{2} + 2 x}$

Solve the equation.

Set the numerator equal to zero.

$4 x + 8 = 0$

Solve the equation for $x$ .

Subtract $8$ from both sides of the equation.

$4 x = - 8$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

Exclude the solutions that do not make $0 = \frac{4 x + 8}{x^{2} + 2 x}$ 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 $y$ .

$y = \frac{4 (0) + 8}{{(0)}^{2} + 2 (0)}$

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