Finite Math Examples

Simplify (y^2+6)/(y+5)-(y-4)/(y-2)
Step 1
To write as a fraction with a common denominator, multiply by .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.1
Multiply by .
Step 3.2
Multiply by .
Step 3.3
Reorder the factors of .
Step 4
Combine the numerators over the common denominator.
Step 5
Simplify the numerator.
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Step 5.1
Expand using the FOIL Method.
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Step 5.1.1
Apply the distributive property.
Step 5.1.2
Apply the distributive property.
Step 5.1.3
Apply the distributive property.
Step 5.2
Simplify each term.
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Step 5.2.1
Multiply by by adding the exponents.
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Step 5.2.1.1
Multiply by .
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Step 5.2.1.1.1
Raise to the power of .
Step 5.2.1.1.2
Use the power rule to combine exponents.
Step 5.2.1.2
Add and .
Step 5.2.2
Move to the left of .
Step 5.2.3
Multiply by .
Step 5.3
Apply the distributive property.
Step 5.4
Multiply by .
Step 5.5
Expand using the FOIL Method.
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Step 5.5.1
Apply the distributive property.
Step 5.5.2
Apply the distributive property.
Step 5.5.3
Apply the distributive property.
Step 5.6
Simplify and combine like terms.
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Step 5.6.1
Simplify each term.
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Step 5.6.1.1
Multiply by by adding the exponents.
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Step 5.6.1.1.1
Move .
Step 5.6.1.1.2
Multiply by .
Step 5.6.1.2
Multiply by .
Step 5.6.1.3
Multiply by .
Step 5.6.2
Add and .
Step 5.7
Subtract from .
Step 5.8
Subtract from .
Step 5.9
Add and .