Find the x and y Intercepts f(x)=(x+5)/(3x-12)

$f (x) = \frac{x + 5}{3 x - 12}$

Find the x-intercepts.

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

$0 = \frac{x + 5}{3 x - 12}$

Solve the equation.

Set the numerator equal to zero.

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{(0) + 5}{3 (0) - 12}$

Solve the equation.

Remove parentheses.

$y = \frac{0 + 5}{3 (0) - 12}$

Remove parentheses.

$y = \frac{(0) + 5}{3 (0) - 12}$

Simplify $\frac{(0) + 5}{3 (0) - 12}$ .

Add $0$ and $5$ .

$y = \frac{5}{3 (0) - 12}$

Simplify the denominator.

Multiply $3$ by $0$ .

$y = \frac{5}{0 - 12}$

Subtract $12$ from $0$ .

$y = \frac{5}{- 12}$

Move the negative in front of the fraction.

$y = - \frac{5}{12}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{12})$

List the intersections.

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

y-intercept(s): $(0, - \frac{5}{12})$