Algebra Examples

Divide (3a^3-15a^2b+12ab^2)/(3a^2b)
Step 1
Simplify the numerator.
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Step 1.1
Factor out of .
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Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.1.4
Factor out of .
Step 1.1.5
Factor out of .
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 1.3
Rewrite as .
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
Cancel the common factor of and .
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Step 3.1
Factor out of .
Step 3.2
Cancel the common factors.
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factor.
Step 3.2.3
Rewrite the expression.
Step 4
Expand using the FOIL Method.
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Step 4.1
Apply the distributive property.
Step 4.2
Apply the distributive property.
Step 4.3
Apply the distributive property.
Step 5
Simplify and combine like terms.
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Step 5.1
Simplify each term.
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Step 5.1.1
Multiply by .
Step 5.1.2
Rewrite using the commutative property of multiplication.
Step 5.1.3
Rewrite using the commutative property of multiplication.
Step 5.1.4
Multiply by by adding the exponents.
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Step 5.1.4.1
Move .
Step 5.1.4.2
Multiply by .
Step 5.1.5
Multiply by .
Step 5.2
Subtract from .
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Step 5.2.1
Move .
Step 5.2.2
Subtract from .
Step 6
Split the fraction into two fractions.
Step 7
Split the fraction into two fractions.
Step 8
Cancel the common factor of and .
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Step 8.1
Factor out of .
Step 8.2
Cancel the common factors.
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Step 8.2.1
Factor out of .
Step 8.2.2
Cancel the common factor.
Step 8.2.3
Rewrite the expression.
Step 9
Cancel the common factor of .
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Step 9.1
Cancel the common factor.
Step 9.2
Rewrite the expression.
Step 10
Cancel the common factor of .
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Step 10.1
Cancel the common factor.
Step 10.2
Divide by .
Step 11
Cancel the common factor of and .
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Step 11.1
Factor out of .
Step 11.2
Cancel the common factors.
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Step 11.2.1
Factor out of .
Step 11.2.2
Cancel the common factor.
Step 11.2.3
Rewrite the expression.