Examples

\frac{(x + 1) (x - 6)}{(x - 6) (x + 3)}

$\frac{(x + 1) (x - 6)}{(x - 6) (x + 3)}$

Step 1

Cancel the common factor of

x - 6

$x - 6$ .

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Step 1.1

Cancel the common factor.

\frac{(x + 1) (x - 6)}{(x - 6) (x + 3)}

$\frac{(x + 1) (x - 6)}{(x - 6) (x + 3)}$

Step 1.2

Rewrite the expression.

\frac{x + 1}{x + 3}

$\frac{x + 1}{x + 3}$

\frac{x + 1}{x + 3}

$\frac{x + 1}{x + 3}$

Step 2

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

x - 6

$x - 6$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to

0

$0$ , solve, and substitute back in to

\frac{x + 1}{x + 3}

$\frac{x + 1}{x + 3}$ .

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Step 3.1

Set

x - 6

$x - 6$ equal to

0

$0$ .

x - 6 = 0

$x - 6 = 0$

Step 3.2

Add

6

$6$ to both sides of the equation.

x = 6

$x = 6$

Step 3.3

Substitute

6

$6$ for

x

$x$ in

\frac{x + 1}{x + 3}

$\frac{x + 1}{x + 3}$ and simplify.

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Step 3.3.1

Substitute

6

$6$ for

x

$x$ to find the

y

$y$ coordinate of the hole.

\frac{6 + 1}{6 + 3}

$\frac{6 + 1}{6 + 3}$

Step 3.3.2

Simplify.

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Step 3.3.2.1

Add

6

$6$ and

1

$1$ .

\frac{7}{6 + 3}

$\frac{7}{6 + 3}$

Step 3.3.2.2

Add

6

$6$ and

3

$3$ .

\frac{7}{9}

$\frac{7}{9}$

\frac{7}{9}

$\frac{7}{9}$

\frac{7}{9}

$\frac{7}{9}$

Step 3.4

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

0

$0$ .

(6, \frac{7}{9})

$(6, \frac{7}{9})$

(6, \frac{7}{9})

$(6, \frac{7}{9})$

Step 4

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