Find the x and y Intercepts f(x)=(x^2+4x)/(2x^2-5x)

$f (x) = \frac{x^{2} + 4 x}{2 x^{2} - 5 x}$

Find the x-intercepts.

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

$0 = \frac{x^{2} + 4 x}{2 x^{2} - 5 x}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} + 4 x = 0$

Solve the equation for $x$ .

Factor $x$ out of $x^{2} + 4 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x + 4 x = 0$

Factor $x$ out of $4 x$ .

$x \cdot x + x \cdot 4 = 0$

Factor $x$ out of $x \cdot x + x \cdot 4$ .

$x (x + 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $x (x + 4) = 0$ true.

$x = 0, - 4$

Exclude the solutions that do not make $0 = \frac{x^{2} + 4 x}{2 x^{2} - 5 x}$ true.

$x = - 4$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0)$

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} + 4 (0)}{2 {(0)}^{2} - 5 \cdot 0}$

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): $None$

List the intersections.

x-intercept(s): $(- 4, 0)$

y-intercept(s): $None$