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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$x = 0$

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

$No solution$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

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

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 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$

Step 4