Find the x and y Intercepts f(x)=(2x+8)/(x^2+x-12)

$f (x) = \frac{2 x + 8}{x^{2} + x - 12}$

Find the x-intercepts.

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

$0 = \frac{2 x + 8}{x^{2} + x - 12}$

Solve the equation.

Set the numerator equal to zero.

$2 x + 8 = 0$

Solve the equation for $x$ .

Subtract $8$ from both sides of the equation.

$2 x = - 8$

Divide each term in $2 x = - 8$ by $2$ and simplify.

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x = - 4$

Exclude the solutions that do not make $0 = \frac{2 x + 8}{x^{2} + x - 12}$ 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 $y$ .

$y = \frac{2 (0) + 8}{{(0)}^{2} + 0 - 12}$

Solve the equation.

Remove parentheses.

$y = \frac{2 (0) + 8}{{(0)}^{2} + 0 - 12}$

Remove parentheses.

$y = \frac{2 (0) + 8}{0^{2} + 0 - 12}$

Remove parentheses.

$y = \frac{2 (0) + 8}{{(0)}^{2} + 0 - 12}$

Simplify $\frac{2 (0) + 8}{{(0)}^{2} + 0 - 12}$ .

Simplify the numerator.

Multiply $2$ by $0$ .

$y = \frac{0 + 8}{0^{2} + 0 - 12}$

Add $0$ and $8$ .

$y = \frac{8}{0^{2} + 0 - 12}$

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{8}{0 + 0 - 12}$

Add $0$ and $0$ .

$y = \frac{8}{0 - 12}$

Subtract $12$ from $0$ .

$y = \frac{8}{- 12}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $- 12$ .

Factor $4$ out of $8$ .

$y = \frac{4 (2)}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$y = \frac{4 \cdot 2}{4 \cdot - 3}$

Cancel the common factor.

$y = \frac{4 \cdot 2}{4 \cdot - 3}$

Rewrite the expression.

$y = \frac{2}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{2}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{2}{3})$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{2}{3})$

Find the x and y Intercepts f(x)=(2x+8)/(x^2+x-12)

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