Basic Math Examples

Simplify (((20k^2-7k-3)/(k^2+6k))÷((5k-3)/(k^3-7k-2)))*(k^2-5k+6)/(4k^2-7k-2)
Step 1
Factor by grouping.
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Step 1.1
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 1.1.1
Factor out of .
Step 1.1.2
Rewrite as plus
Step 1.1.3
Apply the distributive property.
Step 1.2
Factor out the greatest common factor from each group.
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Step 1.2.1
Group the first two terms and the last two terms.
Step 1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 2
Factor out of .
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Step 2.1
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Factor out of .
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
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 4.1.4
Multiply by .
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
Combine.
Step 6
Cancel the common factor of .
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Step 6.1
Cancel the common factor.
Step 6.2
Rewrite the expression.
Step 7
Factor out of .
Step 8
Cancel the common factor of .
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Step 8.1
Factor out of .
Step 8.2
Cancel the common factor.
Step 8.3
Rewrite the expression.
Step 9
Multiply by .
Step 10
Combine and .
Step 11
Factor out of .
Step 12
Cancel the common factor of .
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Step 12.1
Factor out of .
Step 12.2
Cancel the common factor.
Step 12.3
Rewrite the expression.
Step 13
Multiply by .