Finite Math Examples

Simplify (x-7)/(2x^2+7x+3)-(x+4)/(2x^2-9x-5)
Step 1
Simplify each term.
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Step 1.1
Factor by grouping.
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Step 1.1.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 1.1.1.1
Factor out of .
Step 1.1.1.2
Rewrite as plus
Step 1.1.1.3
Apply the distributive property.
Step 1.1.1.4
Multiply by .
Step 1.1.2
Factor out the greatest common factor from each group.
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Step 1.1.2.1
Group the first two terms and the last two terms.
Step 1.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 1.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 1.2
Factor by grouping.
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Step 1.2.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 1.2.1.1
Factor out of .
Step 1.2.1.2
Rewrite as plus
Step 1.2.1.3
Apply the distributive property.
Step 1.2.1.4
Multiply by .
Step 1.2.2
Factor out the greatest common factor from each group.
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Step 1.2.2.1
Group the first two terms and the last two terms.
Step 1.2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 1.2.3
Factor the polynomial by factoring out the greatest common factor, .
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
Subtract from .
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
Subtract from .
Step 6.7
Subtract from .
Step 6.8
Add and .
Step 6.9
Subtract from .
Step 6.10
Subtract from .
Step 7
Simplify with factoring out.
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Step 7.1
Factor out of .
Step 7.2
Rewrite as .
Step 7.3
Factor out of .
Step 7.4
Simplify the expression.
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Step 7.4.1
Rewrite as .
Step 7.4.2
Move the negative in front of the fraction.