Pre-Algebra Examples

Divide ((x^2-6x+9)/(x^2-4))÷((x^2-9)/(x^2-8x+12))
Step 1
To divide by a fraction, multiply by its reciprocal.
Step 2
Factor using the perfect square rule.
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Step 2.1
Rewrite as .
Step 2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.3
Rewrite the polynomial.
Step 2.4
Factor using the perfect square trinomial rule , where and .
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
Factor using the AC method.
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Step 4.1
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 4.2
Write the factored form using these integers.
Step 5
Simplify the denominator.
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Step 5.1
Rewrite as .
Step 5.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 6
Combine.
Step 7
Cancel the common factor of and .
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Step 7.1
Factor out of .
Step 7.2
Cancel the common factors.
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Step 7.2.1
Factor out of .
Step 7.2.2
Cancel the common factor.
Step 7.2.3
Rewrite the expression.
Step 8
Cancel the common factor of .
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Step 8.1
Cancel the common factor.
Step 8.2
Rewrite the expression.