Algebra Examples

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

Step 1

Cancel the common factor of $- x + 3$ and $x - 3$ .

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Step 1.1

Factor $- 1$ out of $- x$ .

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

Step 1.2

Rewrite $3$ as $- 1 (- 3)$ .

$f (x) = \frac{- (x) - 1 \cdot - 3}{x - 3}$

Step 1.3

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

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

Step 1.4

Rewrite $- (x - 3)$ as $- 1 (x - 3)$ .

$f (x) = \frac{- 1 (x - 3)}{x - 3}$

Step 1.5

Cancel the common factor.

$f (x) = \frac{- 1 (x - 3)}{x - 3}$

Step 1.6

Divide $- 1$ by $1$ .

$f (x) = - 1$

Step 2

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

$x - 3$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $- 1$ .

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Step 3.1

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

$x - 3 = 0$

Step 3.2

Add $3$ to both sides of the equation.

$x = 3$

Step 3.3

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

$- 1$

Step 3.4

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

$(3, - 1)$

Step 4