Basic Math Examples

Simplify (8v+2)/(3v^2-3v-18)+9/(3v^2-12v+9)
Step 1
Simplify each term.
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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 1.2
Simplify the denominator.
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Step 1.2.1
Factor out of .
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Step 1.2.1.1
Factor out of .
Step 1.2.1.2
Factor out of .
Step 1.2.1.3
Factor out of .
Step 1.2.1.4
Factor out of .
Step 1.2.1.5
Factor out of .
Step 1.2.2
Factor using the AC method.
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Step 1.2.2.1
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 1.2.2.2
Write the factored form using these integers.
Step 1.3
Cancel the common factor of and .
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Step 1.3.1
Factor out of .
Step 1.3.2
Cancel the common factors.
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Step 1.3.2.1
Factor out of .
Step 1.3.2.2
Factor out of .
Step 1.3.2.3
Factor out of .
Step 1.3.2.4
Factor out of .
Step 1.3.2.5
Factor out of .
Step 1.3.2.6
Cancel the common factor.
Step 1.3.2.7
Rewrite the expression.
Step 1.4
Factor using the AC method.
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Step 1.4.1
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 1.4.2
Write the factored form using these integers.
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
Reorder the factors of .
Step 4.4
Reorder the factors of .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
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Step 6.1
Apply the distributive property.
Step 6.2
Multiply by .
Step 6.3
Multiply by .
Step 6.4
Expand using the FOIL Method.
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Step 6.4.1
Apply the distributive property.
Step 6.4.2
Apply the distributive property.
Step 6.4.3
Apply the distributive property.
Step 6.5
Simplify and combine like terms.
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Step 6.5.1
Simplify each term.
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Step 6.5.1.1
Multiply by by adding the exponents.
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Step 6.5.1.1.1
Move .
Step 6.5.1.1.2
Multiply by .
Step 6.5.1.2
Multiply by .
Step 6.5.1.3
Multiply by .
Step 6.5.2
Add and .
Step 6.6
Multiply by .
Step 6.7
Apply the distributive property.
Step 6.8
Multiply by .
Step 6.9
Add and .
Step 6.10
Add and .