Pre-Algebra Examples

Divide ((12k^2-5k-2)/(k^2+9k))÷((3k^2)/(k^3+7k^2-18k))
Step 1
To divide by a fraction, multiply by its reciprocal.
Step 2
Factor by grouping.
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Step 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 2.1.1
Factor out of .
Step 2.1.2
Rewrite as plus
Step 2.1.3
Apply the distributive property.
Step 2.2
Factor out the greatest common factor from each group.
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Step 2.2.1
Group the first two terms and the last two terms.
Step 2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 2.3
Factor the polynomial by factoring out the greatest common factor, .
Step 3
Factor out of .
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Step 3.1
Factor out of .
Step 3.2
Factor out of .
Step 3.3
Factor out of .
Step 4
Simplify the numerator.
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Step 4.1
Factor out of .
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Step 4.1.1
Factor out of .
Step 4.1.2
Factor out of .
Step 4.1.3
Factor out of .
Step 4.1.4
Factor out of .
Step 4.1.5
Factor out of .
Step 4.2
Factor using the AC method.
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Step 4.2.1
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 4.2.2
Write the factored form using these integers.
Step 5
Combine.
Step 6
Multiply by by adding the exponents.
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Step 6.1
Move .
Step 6.2
Multiply by .
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Step 6.2.1
Raise to the power of .
Step 6.2.2
Use the power rule to combine exponents.
Step 6.3
Add and .
Step 7
Cancel the common factor of and .
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Step 7.1
Factor out of .
Step 7.2
Cancel the common factors.
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Step 7.2.1
Factor out of .
Step 7.2.2
Cancel the common factor.
Step 7.2.3
Rewrite the expression.
Step 8
Cancel the common factor of .
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Step 8.1
Cancel the common factor.
Step 8.2
Rewrite the expression.
Step 9
Move to the left of .
Step 10
Expand using the FOIL Method.
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Step 10.1
Apply the distributive property.
Step 10.2
Apply the distributive property.
Step 10.3
Apply the distributive property.
Step 11
Simplify and combine like terms.
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Step 11.1
Simplify each term.
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Step 11.1.1
Rewrite using the commutative property of multiplication.
Step 11.1.2
Multiply by by adding the exponents.
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Step 11.1.2.1
Move .
Step 11.1.2.2
Multiply by .
Step 11.1.3
Multiply by .
Step 11.1.4
Multiply by .
Step 11.1.5
Multiply by .
Step 11.1.6
Multiply by .
Step 11.2
Add and .
Step 12
Expand by multiplying each term in the first expression by each term in the second expression.
Step 13
Simplify each term.
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Step 13.1
Multiply by by adding the exponents.
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Step 13.1.1
Move .
Step 13.1.2
Multiply by .
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Step 13.1.2.1
Raise to the power of .
Step 13.1.2.2
Use the power rule to combine exponents.
Step 13.1.3
Add and .
Step 13.2
Multiply by .
Step 13.3
Multiply by by adding the exponents.
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Step 13.3.1
Move .
Step 13.3.2
Multiply by .
Step 13.4
Multiply by .
Step 13.5
Multiply by .
Step 14
Subtract from .
Step 15
Subtract from .
Step 16
Split the fraction into two fractions.
Step 17
Split the fraction into two fractions.
Step 18
Split the fraction into two fractions.
Step 19
Cancel the common factor of and .
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Step 19.1
Factor out of .
Step 19.2
Cancel the common factors.
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Step 19.2.1
Factor out of .
Step 19.2.2
Cancel the common factor.
Step 19.2.3
Rewrite the expression.
Step 20
Cancel the common factor of and .
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Step 20.1
Factor out of .
Step 20.2
Cancel the common factors.
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Step 20.2.1
Multiply by .
Step 20.2.2
Cancel the common factor.
Step 20.2.3
Rewrite the expression.
Step 20.2.4
Divide by .
Step 21
Cancel the common factor of .
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Step 21.1
Cancel the common factor.
Step 21.2
Rewrite the expression.
Step 22
Move the negative in front of the fraction.
Step 23
Cancel the common factor of and .
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Step 23.1
Factor out of .
Step 23.2
Cancel the common factors.
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Step 23.2.1
Factor out of .
Step 23.2.2
Cancel the common factor.
Step 23.2.3
Rewrite the expression.