Finite Math Examples

Simplify (x+5)/(x^2+x-12)-(x-7)/(x^2+7x+12)
Step 1
Simplify each term.
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Step 1.1
Factor using the AC method.
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Step 1.1.1
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 1.1.2
Write the factored form using these integers.
Step 1.2
Factor using the AC method.
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Step 1.2.1
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 1.2.2
Write the factored form using these integers.
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
Reorder the factors of .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
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Step 6.1
Expand using the FOIL Method.
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Step 6.1.1
Apply the distributive property.
Step 6.1.2
Apply the distributive property.
Step 6.1.3
Apply the distributive property.
Step 6.2
Simplify and combine like terms.
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Step 6.2.1
Simplify each term.
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Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Move to the left of .
Step 6.2.1.3
Multiply by .
Step 6.2.2
Add and .
Step 6.3
Apply the distributive property.
Step 6.4
Multiply by .
Step 6.5
Expand using the FOIL Method.
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Step 6.5.1
Apply the distributive property.
Step 6.5.2
Apply the distributive property.
Step 6.5.3
Apply the distributive property.
Step 6.6
Simplify and combine like terms.
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Step 6.6.1
Simplify each term.
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Step 6.6.1.1
Multiply by by adding the exponents.
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Step 6.6.1.1.1
Move .
Step 6.6.1.1.2
Multiply by .
Step 6.6.1.2
Multiply by .
Step 6.6.1.3
Multiply by .
Step 6.6.2
Add and .
Step 6.7
Subtract from .
Step 6.8
Add and .
Step 6.9
Add and .
Step 6.10
Subtract from .
Step 6.11
Factor out of .
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Step 6.11.1
Factor out of .
Step 6.11.2
Factor out of .
Step 6.11.3
Factor out of .