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Algebra Examples
Step 1
Step 1.1
Factor out of .
Step 1.2
Factor out of .
Step 1.3
Factor out of .
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
Factor out of .
Step 3.2
Rewrite as .
Step 3.3
Factor out of .
Step 3.4
Rewrite as .
Step 3.5
Cancel the common factor.
Step 3.6
Rewrite the expression.
Step 4
Multiply by .
Step 5
Move the negative in front of the fraction.
Step 6
To find the holes in the graph, look at the denominator factors that were cancelled.
Step 7
Step 7.1
Set equal to .
Step 7.2
Add to both sides of the equation.
Step 7.3
Substitute for in and simplify.
Step 7.3.1
Substitute for to find the coordinate of the hole.
Step 7.3.2
Simplify.
Step 7.3.2.1
Cancel the common factor of and .
Step 7.3.2.1.1
Factor out of .
Step 7.3.2.1.2
Cancel the common factors.
Step 7.3.2.1.2.1
Factor out of .
Step 7.3.2.1.2.2
Factor out of .
Step 7.3.2.1.2.3
Factor out of .
Step 7.3.2.1.2.4
Cancel the common factor.
Step 7.3.2.1.2.5
Rewrite the expression.
Step 7.3.2.2
Subtract from .
Step 7.3.2.3
Divide by .
Step 7.3.2.4
Multiply by .
Step 7.4
The holes in the graph are the points where any of the cancelled factors are equal to .
Step 8