Pre-Algebra Examples

Add (x+8)/(x^2-4x+4)+(3x-2)/(x^2-4)
Step 1
Simplify each term.
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Step 1.1
Factor using the perfect square rule.
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Step 1.1.1
Rewrite as .
Step 1.1.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 1.1.3
Rewrite the polynomial.
Step 1.1.4
Factor using the perfect square trinomial rule , where and .
Step 1.2
Simplify the denominator.
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Step 1.2.1
Rewrite as .
Step 1.2.2
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
Raise to the power of .
Step 4.4
Raise to the power of .
Step 4.5
Use the power rule to combine exponents.
Step 4.6
Add and .
Step 4.7
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
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
Move to the left of .
Step 6.2.1.3
Multiply by .
Step 6.2.2
Add and .
Step 6.3
Expand using the FOIL Method.
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Step 6.3.1
Apply the distributive property.
Step 6.3.2
Apply the distributive property.
Step 6.3.3
Apply the distributive property.
Step 6.4
Simplify and combine like terms.
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Step 6.4.1
Simplify each term.
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Step 6.4.1.1
Multiply by by adding the exponents.
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Step 6.4.1.1.1
Move .
Step 6.4.1.1.2
Multiply by .
Step 6.4.1.2
Multiply by .
Step 6.4.1.3
Multiply by .
Step 6.4.2
Subtract from .
Step 6.5
Add and .
Step 6.6
Subtract from .
Step 6.7
Add and .
Step 6.8
Factor out of .
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Step 6.8.1
Factor out of .
Step 6.8.2
Factor out of .
Step 6.8.3
Factor out of .
Step 6.8.4
Factor out of .
Step 6.8.5
Factor out of .