Find the x and y Intercepts f(x)=(x^2+5x)/(-2x^2+7x)

$f (x) = \frac{x^{2} + 5 x}{- 2 x^{2} + 7 x}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x^{2} + 5 x}{- 2 x^{2} + 7 x}$

Solve the equation.

Set the numerator equal to zero.

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

Solve the equation for $x$ .

Factor $x$ out of $x^{2} + 5 x$ .

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

$x \cdot x + 5 x = 0$

Factor $x$ out of $5 x$ .

$x \cdot x + x \cdot 5 = 0$

Factor $x$ out of $x \cdot x + x \cdot 5$ .

$x (x + 5) = 0$

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

$x = 0$

$x + 5 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $x (x + 5) = 0$ true.

$x = 0, - 5$

Exclude the solutions that do not make $0 = \frac{x^{2} + 5 x}{- 2 x^{2} + 7 x}$ true.

$x = - 5$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} + 5 (0)}{- 2 {(0)}^{2} + 7 (0)}$

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): $(- 5, 0)$

y-intercept(s): $None$

Step 4