Find the x and y Intercepts f(x)=(5x+10)/(x^2+2x)

$f (x) = \frac{5 x + 10}{x^{2} + 2 x}$

Find the x-intercepts.

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

$0 = \frac{5 x + 10}{x^{2} + 2 x}$

Solve the equation.

Set the numerator equal to zero.

$5 x + 10 = 0$

Solve the equation for $x$ .

Subtract $10$ from both sides of the equation.

$5 x = - 10$

Divide each term in $5 x = - 10$ by $5$ and simplify.

Divide each term in $5 x = - 10$ by $5$ .

$\frac{5 x}{5} = \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 10}{5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$x = - 2$

Exclude the solutions that do not make $0 = \frac{5 x + 10}{x^{2} + 2 x}$ true.

$No solution$

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = \frac{5 (0) + 10}{{(0)}^{2} + 2 (0)}$

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): $None$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$