Precalculus 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.

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

Step 1.2

Divide

$3 x + 1$ by

$1$ .

$y = 3 x + 1$

Step 2

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

$x - 1$

Step 3

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

$0$ , solve, and substitute back in to

$3 x + 1$ .

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Step 3.1

Set

$x - 1$ equal to

$0$ .

$x - 1 = 0$

Step 3.2

Add

$1$ to both sides of the equation.

$x = 1$

Step 3.3

Substitute

$1$ for

$x$ in

$3 x + 1$ and simplify.

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Step 3.3.1

Substitute

$1$ for

$x$ to find the

$y$ coordinate of the hole.

$3 \cdot 1 + 1$

Step 3.3.2

Simplify.

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Step 3.3.2.1

Multiply

$3$ by

$1$ .

$3 + 1$

Step 3.3.2.2

Add

$3$ and

$1$ .

$4$

Step 3.4

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

$0$ .

$(1, 4)$

Step 4

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