Basic Math Examples

Simplify 1/(n^2)+1/((n+1)^2)+1
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
Rewrite as .
Step 5.2
Expand using the FOIL Method.
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Step 5.2.1
Apply the distributive property.
Step 5.2.2
Apply the distributive property.
Step 5.2.3
Apply the distributive property.
Step 5.3
Simplify and combine like terms.
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Step 5.3.1
Simplify each term.
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Step 5.3.1.1
Multiply by .
Step 5.3.1.2
Multiply by .
Step 5.3.1.3
Multiply by .
Step 5.3.1.4
Multiply by .
Step 5.3.2
Add and .
Step 5.4
Add and .
Step 6
Combine into one fraction.
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Step 6.1
Write as a fraction with a common denominator.
Step 6.2
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Rewrite as .
Step 7.2
Expand using the FOIL Method.
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Step 7.2.1
Apply the distributive property.
Step 7.2.2
Apply the distributive property.
Step 7.2.3
Apply the distributive property.
Step 7.3
Simplify and combine like terms.
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Step 7.3.1
Simplify each term.
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Step 7.3.1.1
Multiply by .
Step 7.3.1.2
Multiply by .
Step 7.3.1.3
Multiply by .
Step 7.3.1.4
Multiply by .
Step 7.3.2
Add and .
Step 7.4
Apply the distributive property.
Step 7.5
Simplify.
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Step 7.5.1
Multiply by by adding the exponents.
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Step 7.5.1.1
Use the power rule to combine exponents.
Step 7.5.1.2
Add and .
Step 7.5.2
Rewrite using the commutative property of multiplication.
Step 7.5.3
Multiply by .
Step 7.6
Multiply by by adding the exponents.
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Step 7.6.1
Move .
Step 7.6.2
Multiply by .
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Step 7.6.2.1
Raise to the power of .
Step 7.6.2.2
Use the power rule to combine exponents.
Step 7.6.3
Add and .
Step 7.7
Add and .
Step 7.8
Reorder terms.