Finite Math Examples

Simplify (((12y^2-7y-12)/(12y^2+25y+12))/(12y^2-25y+12))/(16y^2-24y+9)
Step 1
Multiply the numerator by the reciprocal of the denominator.
Step 2
Multiply the numerator by the reciprocal of the denominator.
Step 3
Factor by grouping.
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Step 3.1
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 3.1.1
Factor out of .
Step 3.1.2
Rewrite as plus
Step 3.1.3
Apply the distributive property.
Step 3.2
Factor out the greatest common factor from each group.
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Step 3.2.1
Group the first two terms and the last two terms.
Step 3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4
Factor by grouping.
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Step 4.1
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 4.1.1
Factor out of .
Step 4.1.2
Rewrite as plus
Step 4.1.3
Apply the distributive property.
Step 4.2
Factor out the greatest common factor from each group.
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Step 4.2.1
Group the first two terms and the last two terms.
Step 4.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.3
Factor the polynomial by factoring out the greatest common factor, .
Step 5
Cancel the common factor of .
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Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Factor by grouping.
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Step 6.1
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 6.1.1
Factor out of .
Step 6.1.2
Rewrite as plus
Step 6.1.3
Apply the distributive property.
Step 6.2
Factor out the greatest common factor from each group.
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Step 6.2.1
Group the first two terms and the last two terms.
Step 6.2.2
Factor out the greatest common factor (GCF) from each group.
Step 6.3
Factor the polynomial by factoring out the greatest common factor, .
Step 7
Simplify terms.
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Step 7.1
Cancel the common factor of .
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Step 7.1.1
Factor out of .
Step 7.1.2
Cancel the common factor.
Step 7.1.3
Rewrite the expression.
Step 7.2
Multiply by .
Step 8
Factor using the perfect square rule.
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Step 8.1
Rewrite as .
Step 8.2
Rewrite as .
Step 8.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 8.4
Rewrite the polynomial.
Step 8.5
Factor using the perfect square trinomial rule , where and .
Step 9
Combine.
Step 10
Multiply by by adding the exponents.
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Step 10.1
Move .
Step 10.2
Multiply by .
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Step 10.2.1
Raise to the power of .
Step 10.2.2
Use the power rule to combine exponents.
Step 10.3
Add and .
Step 11
Multiply by .