Algebra Examples

Evaluate ( square root of 7+ square root of 2)/( square root of 7- square root of 2)
Step 1
Multiply by .
Step 2
Combine fractions.
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Step 2.1
Multiply by .
Step 2.2
Expand the denominator using the FOIL method.
Step 2.3
Simplify.
Step 3
Simplify the numerator.
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Step 3.1
Raise to the power of .
Step 3.2
Raise to the power of .
Step 3.3
Use the power rule to combine exponents.
Step 3.4
Add and .
Step 4
Rewrite as .
Step 5
Expand using the FOIL Method.
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Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Apply the distributive property.
Step 6
Simplify and combine like terms.
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Step 6.1
Simplify each term.
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Step 6.1.1
Combine using the product rule for radicals.
Step 6.1.2
Multiply by .
Step 6.1.3
Rewrite as .
Step 6.1.4
Pull terms out from under the radical, assuming positive real numbers.
Step 6.1.5
Combine using the product rule for radicals.
Step 6.1.6
Multiply by .
Step 6.1.7
Combine using the product rule for radicals.
Step 6.1.8
Multiply by .
Step 6.1.9
Combine using the product rule for radicals.
Step 6.1.10
Multiply by .
Step 6.1.11
Rewrite as .
Step 6.1.12
Pull terms out from under the radical, assuming positive real numbers.
Step 6.2
Add and .
Step 6.3
Add and .
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: