Algebra Examples

Evaluate (x+y)/(x-y)+1/(x+y)-(x^2+y^2)/(x^2-y^2)
Step 1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
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
Simplify terms.
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Step 5.1
Combine the numerators over the common denominator.
Step 5.2
Combine the numerators over the common denominator.
Step 6
Simplify each term.
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Step 6.1
Expand using the FOIL Method.
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Step 6.1.1
Apply the distributive property.
Step 6.1.2
Apply the distributive property.
Step 6.1.3
Apply the distributive property.
Step 6.2
Simplify and combine like terms.
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Step 6.2.1
Simplify each term.
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Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Multiply by .
Step 6.2.2
Add and .
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Step 6.2.2.1
Reorder and .
Step 6.2.2.2
Add and .
Step 6.3
Apply the distributive property.
Step 7
Combine the opposite terms in .
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Step 7.1
Subtract from .
Step 7.2
Add and .
Step 7.3
Subtract from .
Step 7.4
Add and .