Basic Math Examples

Simplify z/(z^2-4)-(4z-4)/(z^2+6z+8)
Step 1
Simplify each term.
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Step 1.1
Simplify the denominator.
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Step 1.1.1
Rewrite as .
Step 1.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.2
Factor out of .
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Step 1.2.1
Factor out of .
Step 1.2.2
Factor out of .
Step 1.2.3
Factor out of .
Step 1.3
Factor using the AC method.
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Step 1.3.1
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 1.3.2
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 .
Step 6.3
Move to the left of .
Step 6.4
Apply the distributive property.
Step 6.5
Multiply by .
Step 6.6
Expand using the FOIL Method.
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Step 6.6.1
Apply the distributive property.
Step 6.6.2
Apply the distributive property.
Step 6.6.3
Apply the distributive property.
Step 6.7
Simplify and combine like terms.
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Step 6.7.1
Simplify each term.
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Step 6.7.1.1
Multiply by by adding the exponents.
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Step 6.7.1.1.1
Move .
Step 6.7.1.1.2
Multiply by .
Step 6.7.1.2
Multiply by .
Step 6.7.1.3
Multiply by .
Step 6.7.2
Add and .
Step 6.8
Subtract from .
Step 6.9
Add and .
Step 7
Simplify with factoring out.
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Step 7.1
Factor out of .
Step 7.2
Factor out of .
Step 7.3
Factor out of .
Step 7.4
Rewrite as .
Step 7.5
Factor out of .
Step 7.6
Simplify the expression.
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Step 7.6.1
Rewrite as .
Step 7.6.2
Move the negative in front of the fraction.