Algebra Examples

Simplify Simplify ((x^2+3x+2)/(x^2-1))÷((x^2+6x)/(x^2-x))
Simplify
Step 1
To divide by a fraction, multiply by its reciprocal.
Step 2
Factor using the AC method.
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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
Simplify the denominator.
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Step 3.1
Rewrite as .
Step 3.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4
Simplify terms.
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Step 4.1
Cancel the common factor of .
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Step 4.1.1
Cancel the common factor.
Step 4.1.2
Rewrite the expression.
Step 4.2
Factor out of .
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Step 4.2.1
Factor out of .
Step 4.2.2
Factor out of .
Step 4.2.3
Factor out of .
Step 4.3
Factor out of .
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Step 4.3.1
Factor out of .
Step 4.3.2
Factor out of .
Step 4.3.3
Factor out of .
Step 4.4
Cancel the common factor of .
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Step 4.4.1
Factor out of .
Step 4.4.2
Cancel the common factor.
Step 4.4.3
Rewrite the expression.
Step 4.5
Cancel the common factor of .
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Step 4.5.1
Cancel the common factor.
Step 4.5.2
Rewrite the expression.
Step 4.6
Multiply by .