Algebra Examples

Simplify the Radical Expression (3+ square root of 8)/(2-2 square root of 8)
Step 1
Simplify the numerator.
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Step 1.1
Rewrite as .
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Step 1.1.1
Factor out of .
Step 1.1.2
Rewrite as .
Step 1.2
Pull terms out from under the radical.
Step 1.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2
Simplify the denominator.
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Step 2.1
Rewrite as .
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Step 2.1.1
Factor out of .
Step 2.1.2
Rewrite as .
Step 2.2
Pull terms out from under the radical.
Step 2.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.4
Multiply by .
Step 3
Multiply by .
Step 4
Multiply by .
Step 5
Expand the denominator using the FOIL method.
Step 6
Simplify.
Step 7
Cancel the common factor of and .
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Step 7.1
Factor out of .
Step 7.2
Cancel the common factors.
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Step 7.2.1
Factor out of .
Step 7.2.2
Cancel the common factor.
Step 7.2.3
Rewrite the expression.
Step 8
Expand using the FOIL Method.
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Step 8.1
Apply the distributive property.
Step 8.2
Apply the distributive property.
Step 8.3
Apply the distributive property.
Step 9
Simplify and combine like terms.
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Step 9.1
Simplify each term.
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Step 9.1.1
Multiply by .
Step 9.1.2
Multiply by .
Step 9.1.3
Multiply by .
Step 9.1.4
Multiply .
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Step 9.1.4.1
Multiply by .
Step 9.1.4.2
Raise to the power of .
Step 9.1.4.3
Raise to the power of .
Step 9.1.4.4
Use the power rule to combine exponents.
Step 9.1.4.5
Add and .
Step 9.1.5
Rewrite as .
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Step 9.1.5.1
Use to rewrite as .
Step 9.1.5.2
Apply the power rule and multiply exponents, .
Step 9.1.5.3
Combine and .
Step 9.1.5.4
Cancel the common factor of .
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Step 9.1.5.4.1
Cancel the common factor.
Step 9.1.5.4.2
Rewrite the expression.
Step 9.1.5.5
Evaluate the exponent.
Step 9.1.6
Multiply by .
Step 9.2
Add and .
Step 9.3
Add and .
Step 10
Move the negative in front of the fraction.
Step 11
The result can be shown in multiple forms.
Exact Form:
Decimal Form: