Basic Math Examples

Simplify 6/(c+3)+3/(c^2-3c+9)-162/(c^3+27)
Step 1
Simplify the denominator.
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Step 1.1
Rewrite as .
Step 1.2
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Step 1.3
Simplify.
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Step 1.3.1
Multiply by .
Step 1.3.2
Raise to the power of .
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
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Simplify each term.
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Step 7.1.1
Apply the distributive property.
Step 7.1.2
Simplify.
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Step 7.1.2.1
Multiply by .
Step 7.1.2.2
Multiply by .
Step 7.1.3
Apply the distributive property.
Step 7.1.4
Multiply by .
Step 7.2
Add and .
Step 7.3
Add and .
Step 7.4
Subtract from .
Step 8
Simplify the numerator.
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Step 8.1
Factor out of .
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Step 8.1.1
Factor out of .
Step 8.1.2
Factor out of .
Step 8.1.3
Factor out of .
Step 8.1.4
Factor out of .
Step 8.1.5
Factor out of .
Step 8.2
Factor by grouping.
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Step 8.2.1
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 8.2.1.1
Factor out of .
Step 8.2.1.2
Rewrite as plus
Step 8.2.1.3
Apply the distributive property.
Step 8.2.2
Factor out the greatest common factor from each group.
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Step 8.2.2.1
Group the first two terms and the last two terms.
Step 8.2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 8.2.3
Factor the polynomial by factoring out the greatest common factor, .
Step 9
Cancel the common factor of .
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Step 9.1
Cancel the common factor.
Step 9.2
Rewrite the expression.