Basic Math Examples

Simplify ((16a^2-28a+12)/(a^4-3a^3))÷((3-4a)/(4a^3))*(a-3)/(4a-4)
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
Factor out of .
Step 1.2.1.2
Rewrite as plus
Step 1.2.1.3
Apply the distributive property.
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
Simplify with factoring out.
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Step 2.1
Factor out of .
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Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.2
Factor out of .
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Step 2.2.1
Factor out of .
Step 2.2.2
Factor out of .
Step 2.2.3
Factor out of .
Step 3
To divide by a fraction, multiply by its reciprocal.
Step 4
Cancel the common factor of .
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Step 4.1
Factor out of .
Step 4.2
Cancel the common factor.
Step 4.3
Rewrite the expression.
Step 5
Multiply by .
Step 6
Multiply by .
Step 7
Cancel the common factor of .
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Step 7.1
Factor out of .
Step 7.2
Cancel the common factor.
Step 7.3
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
Cancel the common factor of and .
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Step 9.1
Factor out of .
Step 9.2
Rewrite as .
Step 9.3
Factor out of .
Step 9.4
Rewrite as .
Step 9.5
Reorder terms.
Step 9.6
Cancel the common factor.
Step 9.7
Divide by .
Step 10
Multiply by .