Finite Math Examples

Simplify (3m)/(6m^2+13mn+6n^2)+(2m)/(4m^2+8mn+3n^2)
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
Reorder terms.
Step 1.1.1.2
Reorder and .
Step 1.1.1.3
Factor out of .
Step 1.1.1.4
Rewrite as plus
Step 1.1.1.5
Apply the distributive property.
Step 1.1.1.6
Move parentheses.
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
Reorder terms.
Step 1.2.1.2
Reorder and .
Step 1.2.1.3
Factor out of .
Step 1.2.1.4
Rewrite as plus
Step 1.2.1.5
Apply the distributive property.
Step 1.2.1.6
Move parentheses.
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 4.4
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
Factor out of .
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Step 6.1.1
Factor out of .
Step 6.1.2
Factor out of .
Step 6.1.3
Factor out of .
Step 6.2
Apply the distributive property.
Step 6.3
Multiply by .
Step 6.4
Apply the distributive property.
Step 6.5
Multiply by .
Step 6.6
Multiply by .
Step 6.7
Add and .
Step 6.8
Add and .