Basic Math Examples

Simplify ((21y^2+4y-1)/(5y+3))/((3y+1)/(10y^2+y-3))
Step 1
Multiply the numerator by the reciprocal of the denominator.
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
Cancel the common factor of .
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Step 3.1
Factor out of .
Step 3.2
Cancel the common factor.
Step 3.3
Rewrite the expression.
Step 4
Multiply by .
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
Multiply by .
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
Cancel the common factor of .
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Step 6.1
Cancel the common factor.
Step 6.2
Divide by .
Step 7
Expand using the FOIL Method.
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Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Apply the distributive property.
Step 8
Simplify and combine like terms.
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Step 8.1
Simplify each term.
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Step 8.1.1
Rewrite using the commutative property of multiplication.
Step 8.1.2
Multiply by by adding the exponents.
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Step 8.1.2.1
Move .
Step 8.1.2.2
Multiply by .
Step 8.1.3
Multiply by .
Step 8.1.4
Multiply by .
Step 8.1.5
Multiply by .
Step 8.1.6
Multiply by .
Step 8.2
Subtract from .