# Calculus Examples

Step 1

Step 1.1

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Step 1.2

Write the factored form using these integers.

Step 2

Step 2.1

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Step 2.2

Write the factored form using these integers.

Step 3

Step 3.1

Cancel the common factor.

Step 3.2

Rewrite the expression.

Step 4

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

Step 5

Step 5.1

Set equal to .

Step 5.2

Add to both sides of the equation.

Step 5.3

Substitute for in and simplify.

Step 5.3.1

Substitute for to find the coordinate of the hole.

Step 5.3.2

Simplify.

Step 5.3.2.1

Add and .

Step 5.3.2.2

Subtract from .

Step 5.3.2.3

Move the negative in front of the fraction.

Step 5.4

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

Step 6