Find the x and y Intercepts f(x)=(3x)/(x^2-x-2)

$f (x) = \frac{3 x}{x^{2} - x - 2}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3 x}{x^{2} - x - 2}$

Solve the equation.

Set the numerator equal to zero.

$3 x = 0$

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{3 (0)}{{(0)}^{2} - (0) - 2}$

Solve the equation.

Remove parentheses.

$y = \frac{3 (0)}{0^{2} - (0) - 2}$

Remove parentheses.

$y = \frac{3 (0)}{{(0)}^{2} - (0) - 2}$

Simplify $\frac{3 (0)}{{(0)}^{2} - (0) - 2}$ .

Multiply $3$ by $0$ .

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

Simplify the denominator.

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

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

Multiply $- 1$ by $0$ .

$y = \frac{0}{0 + 0 - 2}$

Add $0$ and $0$ .

$y = \frac{0}{0 - 2}$

Subtract $2$ from $0$ .

$y = \frac{0}{- 2}$

Divide $0$ by $- 2$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 0)$

Step 4

Find the x and y Intercepts f(x)=(3x)/(x^2-x-2)

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