Algebra Examples

$f (x) = \frac{3 x - 9}{x - 3}$

Step 1

Factor $3$ out of $3 x - 9$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$f (x) = \frac{3 (x) - 9}{x - 3}$

Step 1.2

Factor $3$ out of $- 9$ .

$f (x) = \frac{3 x + 3 \cdot - 3}{x - 3}$

Step 1.3

Factor $3$ out of $3 x + 3 \cdot - 3$ .

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

Step 2

Cancel the common factor of $x - 3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $3$ by $1$ .

$f (x) = 3$

Step 3

To find the holes in the graph, look at the denominator factors that were cancelled.

$x - 3$

Step 4

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $3$ .

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Step 4.1

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Step 4.2

Add $3$ to both sides of the equation.

$x = 3$

Step 4.3

Because the cancelled expression is constant with respect to $x$ , it is the $y$ coordinate for every hole.

$3$

Step 4.4

The holes in the graph are the points where any of the cancelled factors are equal to $0$ .

$(3, 3)$

Step 5