Find the x and y Intercepts y=(12-4x)/(x^2-7x+12)

$y = \frac{12 - 4 x}{x^{2} - 7 x + 12}$

Step 1

Find the x-intercepts.

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

$0 = \frac{12 - 4 x}{x^{2} - 7 x + 12}$

Solve the equation.

Set the numerator equal to zero.

$12 - 4 x = 0$

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 $0 = \frac{12 - 4 x}{x^{2} - 7 x + 12}$ true.

$No solution$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = \frac{12 - 4 \cdot 0}{{(0)}^{2} - 7 \cdot 0 + 12}$

Solve the equation.

Remove parentheses.

$y = \frac{12 - 4 \cdot 0}{0^{2} - 7 \cdot 0 + 12}$

Remove parentheses.

$y = \frac{12 - 4 \cdot 0}{{(0)}^{2} - 7 \cdot 0 + 12}$

Simplify $\frac{12 - 4 \cdot 0}{{(0)}^{2} - 7 \cdot 0 + 12}$ .

Simplify the numerator.

Multiply $- 4$ by $0$ .

$y = \frac{12 + 0}{0^{2} - 7 \cdot 0 + 12}$

Add $12$ and $0$ .

$y = \frac{12}{0^{2} - 7 \cdot 0 + 12}$

Simplify the denominator.

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

$y = \frac{12}{0 - 7 \cdot 0 + 12}$

Multiply $- 7$ by $0$ .

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

Add $0$ and $0$ .

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

Add $0$ and $12$ .

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

Divide $12$ by $12$ .

$y = 1$

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 1)$

Step 4

Find the x and y Intercepts y=(12-4x)/(x^2-7x+12)

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