Find the x and y Intercepts f(x)=(3x-6)/(x^2-6x+8)

$f (x) = \frac{3 x - 6}{x^{2} - 6 x + 8}$

Find the x-intercepts.

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

$0 = \frac{3 x - 6}{x^{2} - 6 x + 8}$

Solve the equation.

Set the numerator equal to zero.

$3 x - 6 = 0$

Solve the equation for $x$ .

Add $6$ to both sides of the equation.

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

Exclude the solutions that do not make $0 = \frac{3 x - 6}{x^{2} - 6 x + 8}$ 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 $y$ .

$y = \frac{3 (0) - 6}{{(0)}^{2} - 6 \cdot 0 + 8}$

Solve the equation.

Remove parentheses.

$y = \frac{3 (0) - 6}{0^{2} - 6 \cdot 0 + 8}$

Remove parentheses.

$y = \frac{3 (0) - 6}{{(0)}^{2} - 6 \cdot 0 + 8}$

Simplify $\frac{3 (0) - 6}{{(0)}^{2} - 6 \cdot 0 + 8}$ .

Simplify the numerator.

Multiply $3$ by $0$ .

$y = \frac{0 - 6}{0^{2} - 6 \cdot 0 + 8}$

Subtract $6$ from $0$ .

$y = \frac{- 6}{0^{2} - 6 \cdot 0 + 8}$

Simplify the denominator.

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

$y = \frac{- 6}{0 - 6 \cdot 0 + 8}$

Multiply $- 6$ by $0$ .

$y = \frac{- 6}{0 + 0 + 8}$

Add $0$ and $0$ .

$y = \frac{- 6}{0 + 8}$

Add $0$ and $8$ .

$y = \frac{- 6}{8}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 6$ and $8$ .

Factor $2$ out of $- 6$ .

$y = \frac{2 (- 3)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $None$

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

Find the x and y Intercepts f(x)=(3x-6)/(x^2-6x+8)

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