Precalculus Examples

$\frac{3 x - 3}{x - 2}$

Step 1

Write $\frac{3 x - 3}{x - 2}$ as an equation.

$y = \frac{3 x - 3}{x - 2}$

Step 2

Find the x-intercepts.

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Step 2.1

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$3 x - 3 = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Add $3$ to both sides of the equation.

$3 x = 3$

Step 2.2.2.2

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

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Step 2.2.2.2.1

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

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

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $3$ by $3$ .

$x = 1$

Step 2.3

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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Step 3.1

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

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

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

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

Step 3.2.2

Remove parentheses.

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

Step 3.2.3

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

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Step 3.2.3.1

Simplify the numerator.

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Step 3.2.3.1.1

Multiply $3$ by $0$ .

$y = \frac{0 - 3}{0 - 2}$

Step 3.2.3.1.2

Subtract $3$ from $0$ .

$y = \frac{- 3}{0 - 2}$

Step 3.2.3.2

Reduce the expression by cancelling the common factors.

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Step 3.2.3.2.1

Subtract $2$ from $0$ .

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

Step 3.2.3.2.2

Dividing two negative values results in a positive value.

$y = \frac{3}{2}$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{2})$

Step 4

List the intersections.

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

y-intercept(s): $(0, \frac{3}{2})$

Step 5