Basic Math Examples

Simplify (2y)/(y^2+5y+6)+(y+1)/(y^2+2y-3)
Step 1
Simplify each term.
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Step 1.1
Factor using the AC method.
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Step 1.1.1
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 1.1.2
Write the factored form using these integers.
Step 1.2
Factor using the AC method.
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Step 1.2.1
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
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 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 by adding the exponents.
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Step 6.2.1
Move .
Step 6.2.2
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 .
Step 6.5.1.2
Move to the left of .
Step 6.5.1.3
Multiply by .
Step 6.5.1.4
Multiply by .
Step 6.5.2
Add and .
Step 6.6
Add and .
Step 6.7
Add and .