Trigonometry Examples

$y = \frac{6 - 3 x}{x^{2} - 5 x + 6}$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = \frac{6 - 3 x}{x^{2} - 5 x + 6}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$6 - 3 x = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

Subtract $6$ from both sides of the equation.

$- 3 x = - 6$

Step 1.2.2.2

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

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Step 1.2.2.2.1

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

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

Step 1.2.2.2.2

Simplify the left side.

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Step 1.2.2.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 1.2.2.2.3

Simplify the right side.

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Step 1.2.2.2.3.1

Divide $- 6$ by $- 3$ .

$x = 2$

Step 1.2.3

Exclude the solutions that do not make $0 = \frac{6 - 3 x}{x^{2} - 5 x + 6}$ true.

$No solution$

Step 1.3

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.

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Step 2.1

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

$y = \frac{6 - 3 \cdot 0}{{(0)}^{2} - 5 \cdot 0 + 6}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{6 - 3 \cdot 0}{0^{2} - 5 \cdot 0 + 6}$

Step 2.2.2

Remove parentheses.

$y = \frac{6 - 3 \cdot 0}{{(0)}^{2} - 5 \cdot 0 + 6}$

Step 2.2.3

Simplify $\frac{6 - 3 \cdot 0}{{(0)}^{2} - 5 \cdot 0 + 6}$ .

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Step 2.2.3.1

Simplify the numerator.

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Step 2.2.3.1.1

Multiply $- 3$ by $0$ .

$y = \frac{6 + 0}{0^{2} - 5 \cdot 0 + 6}$

Step 2.2.3.1.2

Add $6$ and $0$ .

$y = \frac{6}{0^{2} - 5 \cdot 0 + 6}$

Step 2.2.3.2

Simplify the denominator.

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Step 2.2.3.2.1

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

$y = \frac{6}{0 - 5 \cdot 0 + 6}$

Step 2.2.3.2.2

Multiply $- 5$ by $0$ .

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

Step 2.2.3.2.3

Add $0$ and $0$ .

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

Step 2.2.3.2.4

Add $0$ and $6$ .

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

Step 2.2.3.3

Divide $6$ by $6$ .

$y = 1$

Step 2.3

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