Basic Math Examples

Simplify ( square root of 22- square root of 5)/( square root of 22+ square root of 5)
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
Multiply .
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Step 6.1.5.1
Combine using the product rule for radicals.
Step 6.1.5.2
Multiply by .
Step 6.1.6
Multiply .
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Step 6.1.6.1
Combine using the product rule for radicals.
Step 6.1.6.2
Multiply by .
Step 6.1.7
Multiply .
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Step 6.1.7.1
Multiply by .
Step 6.1.7.2
Multiply by .
Step 6.1.7.3
Raise to the power of .
Step 6.1.7.4
Raise to the power of .
Step 6.1.7.5
Use the power rule to combine exponents.
Step 6.1.7.6
Add and .
Step 6.1.8
Rewrite as .
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Step 6.1.8.1
Use to rewrite as .
Step 6.1.8.2
Apply the power rule and multiply exponents, .
Step 6.1.8.3
Combine and .
Step 6.1.8.4
Cancel the common factor of .
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Step 6.1.8.4.1
Cancel the common factor.
Step 6.1.8.4.2
Rewrite the expression.
Step 6.1.8.5
Evaluate the exponent.
Step 6.2
Add and .
Step 6.3
Subtract from .
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: