Find the x and y Intercepts f(x)=(4x+12)/(x^2-9)

$f (x) = \frac{4 x + 12}{x^{2} - 9}$

Find the x-intercepts.

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

$0 = \frac{4 x + 12}{x^{2} - 9}$

Solve the equation.

Set the numerator equal to zero.

$4 x + 12 = 0$

Solve the equation for $x$ .

Subtract $12$ from both sides of the equation.

$4 x = - 12$

Divide each term in $4 x = - 12$ by $4$ and simplify.

Divide each term in $4 x = - 12$ by $4$ .

$\frac{4 x}{4} = \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 12}{4}$

Divide $x$ by $1$ .

$x = \frac{- 12}{4}$

Simplify the right side.

Divide $- 12$ by $4$ .

$x = - 3$

Exclude the solutions that do not make $0 = \frac{4 x + 12}{x^{2} - 9}$ 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 $y$ .

$y = \frac{4 (0) + 12}{{(0)}^{2} - 9}$

Solve the equation.

Remove parentheses.

$y = \frac{4 (0) + 12}{0^{2} - 9}$

Remove parentheses.

$y = \frac{4 (0) + 12}{{(0)}^{2} - 9}$

Simplify $\frac{4 (0) + 12}{{(0)}^{2} - 9}$ .

Simplify the numerator.

Multiply $4$ by $0$ .

$y = \frac{0 + 12}{0^{2} - 9}$

Add $0$ and $12$ .

$y = \frac{12}{0^{2} - 9}$

Simplify the denominator.

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

$y = \frac{12}{0 - 9}$

Subtract $9$ from $0$ .

$y = \frac{12}{- 9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $12$ and $- 9$ .

Factor $3$ out of $12$ .

$y = \frac{3 (4)}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{4}{3})$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{4}{3})$

Find the x and y Intercepts f(x)=(4x+12)/(x^2-9)

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