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

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

Step 1

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

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

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

Solve the equation for $x$ .

Factor the left side of the equation.

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

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

$2 (x^{2}) + 2 x - 4 = 0$

Factor $2$ out of $2 x$ .

$2 (x^{2}) + 2 (x) - 4 = 0$

Factor $2$ out of $- 4$ .

$2 (x^{2}) + 2 x + 2 \cdot - 2 = 0$

Factor $2$ out of $2 (x^{2}) + 2 x$ .

$2 (x^{2} + x) + 2 \cdot - 2 = 0$

Factor $2$ out of $2 (x^{2} + x) + 2 \cdot - 2$ .

$2 (x^{2} + x - 2) = 0$

Factor.

Factor $x^{2} + x - 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Write the factored form using these integers.

$2 ((x - 1) (x + 2)) = 0$

Remove unnecessary parentheses.

$2 (x - 1) (x + 2) = 0$

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

$x - 1 = 0$

$x + 2 = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $2 (x - 1) (x + 2) = 0$ true.

$x = 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 2, 0)$

Step 3

Find the y-intercepts.

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

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

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): $(1, 0), (- 2, 0)$

y-intercept(s): $None$

Step 5

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

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