Basic Math Examples

Simplify ((3z^2-2z-5)/(z^2+6z+5))÷((10z^2*(9z)-9)/(2z^2+13z+15))
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 using the AC method.
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Step 3.1
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 3.2
Write the factored form using these integers.
Step 4
Cancel the common factor of .
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Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Factor by grouping.
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Step 5.1
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 5.1.1
Factor out of .
Step 5.1.2
Rewrite as plus
Step 5.1.3
Apply the distributive property.
Step 5.2
Factor out the greatest common factor from each group.
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Step 5.2.1
Group the first two terms and the last two terms.
Step 5.2.2
Factor out the greatest common factor (GCF) from each group.
Step 5.3
Factor the polynomial by factoring out the greatest common factor, .
Step 6
Simplify the denominator.
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Step 6.1
Factor out of .
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Step 6.1.1
Factor out of .
Step 6.1.2
Factor out of .
Step 6.1.3
Factor out of .
Step 6.2
Multiply by by adding the exponents.
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Step 6.2.1
Move .
Step 6.2.2
Multiply by .
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Step 6.2.2.1
Raise to the power of .
Step 6.2.2.2
Use the power rule to combine exponents.
Step 6.2.3
Add and .
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 .