Basic Math Examples

Factor 1/(a^2-25)-(a-5)/(a^2-4a-5)
Step 1
Factor using the AC method.
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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
Cancel the common factor of .
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Step 2.1
Cancel the common factor.
Step 2.2
Rewrite the expression.
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 5.3
Reorder the factors of .
Step 6
Combine the numerators over the common denominator.
Step 7
Rewrite in a factored form.
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Step 7.1
Apply the distributive property.
Step 7.2
Multiply by .
Step 7.3
Add and .
Step 7.4
Reorder terms.
Step 7.5
Factor out of .
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Step 7.5.1
Factor out of .
Step 7.5.2
Factor out of .
Step 7.5.3
Rewrite as .
Step 7.5.4
Factor out of .
Step 7.5.5
Factor out of .
Step 7.6
Rewrite as .
Step 7.7
Factor.
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Step 7.7.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 7.7.2
Remove unnecessary parentheses.