Pre-Algebra Examples

Divide (12mn+32n^2-54m^2)/(8n-9m)
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 2
Cancel the common factor of and .
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Step 2.1
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Factor out of .
Step 2.4
Rewrite as .
Step 2.5
Reorder terms.
Step 2.6
Cancel the common factor.
Step 2.7
Divide by .
Step 3
Apply the distributive property.
Step 4
Multiply by .
Step 5
Multiply by .
Step 6
Apply the distributive property.
Step 7
Multiply by .
Step 8
Multiply by .