Calculus Examples

y = \frac{(3 x + 1) (x - 1)}{x - 1}

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

Step 1

Cancel the common factor of

x - 1

$x - 1$ .

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Step 1.1

Cancel the common factor.

y = \frac{(3 x + 1) (x - 1)}{x - 1}

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

Step 1.2

Divide

3 x + 1

$3 x + 1$ by

1

$1$ .

y = 3 x + 1

$y = 3 x + 1$

y = 3 x + 1

$y = 3 x + 1$

Step 2

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

x - 1

$x - 1$

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

3 x + 1

$3 x + 1$ .

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Step 3.1

Set

x - 1

$x - 1$ equal to

0

$0$ .

x - 1 = 0

$x - 1 = 0$

Step 3.2

Add

1

$1$ to both sides of the equation.

x = 1

$x = 1$

Step 3.3

Substitute

1

$1$ for

x

$x$ in

3 x + 1

$3 x + 1$ and simplify.

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Step 3.3.1

Substitute

1

$1$ for

x

$x$ to find the

y

$y$ coordinate of the hole.

3 \cdot 1 + 1

$3 \cdot 1 + 1$

Step 3.3.2

Simplify.

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Step 3.3.2.1

Multiply

3

$3$ by

1

$1$ .

3 + 1

$3 + 1$

Step 3.3.2.2

Add

3

$3$ and

1

$1$ .

4

$4$

4

$4$

4

$4$

Step 3.4

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

0

$0$ .

(1, 4)

$(1, 4)$

(1, 4)

$(1, 4)$

Step 4

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