Basic Math Examples

Multiply (15/( square root of 6-1)+4/( square root of 6-2)-12/(3- square root of 6))*( square root of 6+11)
Step 1
Find the common denominator.
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Step 1.1
Multiply by .
Step 1.2
Multiply by .
Step 1.3
Multiply by .
Step 1.4
Multiply by .
Step 1.5
Multiply by .
Step 1.6
Multiply by .
Step 1.7
Reorder the factors of .
Step 1.8
Reorder the factors of .
Step 1.9
Reorder the factors of .
Step 2
Simplify terms.
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Step 2.1
Combine the numerators over the common denominator.
Step 2.2
Simplify each term.
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Step 2.2.1
Expand using the FOIL Method.
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Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Apply the distributive property.
Step 2.2.1.3
Apply the distributive property.
Step 2.2.2
Simplify and combine like terms.
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Step 2.2.2.1
Simplify each term.
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Step 2.2.2.1.1
Move to the left of .
Step 2.2.2.1.2
Multiply .
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Step 2.2.2.1.2.1
Raise to the power of .
Step 2.2.2.1.2.2
Raise to the power of .
Step 2.2.2.1.2.3
Use the power rule to combine exponents.
Step 2.2.2.1.2.4
Add and .
Step 2.2.2.1.3
Rewrite as .
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Step 2.2.2.1.3.1
Use to rewrite as .
Step 2.2.2.1.3.2
Apply the power rule and multiply exponents, .
Step 2.2.2.1.3.3
Combine and .
Step 2.2.2.1.3.4
Cancel the common factor of .
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Step 2.2.2.1.3.4.1
Cancel the common factor.
Step 2.2.2.1.3.4.2
Rewrite the expression.
Step 2.2.2.1.3.5
Evaluate the exponent.
Step 2.2.2.1.4
Multiply by .
Step 2.2.2.1.5
Multiply by .
Step 2.2.2.1.6
Multiply by .
Step 2.2.2.2
Add and .
Step 2.2.2.3
Subtract from .
Step 2.2.3
Apply the distributive property.
Step 2.2.4
Multiply by .
Step 2.2.5
Multiply by .
Step 2.2.6
Expand using the FOIL Method.
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Step 2.2.6.1
Apply the distributive property.
Step 2.2.6.2
Apply the distributive property.
Step 2.2.6.3
Apply the distributive property.
Step 2.2.7
Simplify and combine like terms.
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Step 2.2.7.1
Simplify each term.
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Step 2.2.7.1.1
Move to the left of .
Step 2.2.7.1.2
Multiply .
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Step 2.2.7.1.2.1
Raise to the power of .
Step 2.2.7.1.2.2
Raise to the power of .
Step 2.2.7.1.2.3
Use the power rule to combine exponents.
Step 2.2.7.1.2.4
Add and .
Step 2.2.7.1.3
Rewrite as .
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Step 2.2.7.1.3.1
Use to rewrite as .
Step 2.2.7.1.3.2
Apply the power rule and multiply exponents, .
Step 2.2.7.1.3.3
Combine and .
Step 2.2.7.1.3.4
Cancel the common factor of .
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Step 2.2.7.1.3.4.1
Cancel the common factor.
Step 2.2.7.1.3.4.2
Rewrite the expression.
Step 2.2.7.1.3.5
Evaluate the exponent.
Step 2.2.7.1.4
Multiply by .
Step 2.2.7.1.5
Multiply by .
Step 2.2.7.1.6
Multiply .
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Step 2.2.7.1.6.1
Multiply by .
Step 2.2.7.1.6.2
Multiply by .
Step 2.2.7.2
Add and .
Step 2.2.7.3
Subtract from .
Step 2.2.8
Apply the distributive property.
Step 2.2.9
Multiply by .
Step 2.2.10
Multiply by .
Step 2.2.11
Expand using the FOIL Method.
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Step 2.2.11.1
Apply the distributive property.
Step 2.2.11.2
Apply the distributive property.
Step 2.2.11.3
Apply the distributive property.
Step 2.2.12
Simplify and combine like terms.
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Step 2.2.12.1
Simplify each term.
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Step 2.2.12.1.1
Combine using the product rule for radicals.
Step 2.2.12.1.2
Multiply by .
Step 2.2.12.1.3
Rewrite as .
Step 2.2.12.1.4
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.12.1.5
Move to the left of .
Step 2.2.12.1.6
Rewrite as .
Step 2.2.12.1.7
Multiply by .
Step 2.2.12.2
Add and .
Step 2.2.12.3
Subtract from .
Step 2.2.13
Apply the distributive property.
Step 2.2.14
Multiply by .
Step 2.2.15
Multiply by .
Step 2.3
Simplify by adding terms.
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Step 2.3.1
Subtract from .
Step 2.3.2
Subtract from .
Step 2.3.3
Add and .
Step 2.3.4
Add and .
Step 3
Expand using the FOIL Method.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 4
Simplify and combine like terms.
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Step 4.1
Simplify each term.
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Step 4.1.1
Multiply by .
Step 4.1.2
Multiply .
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Step 4.1.2.1
Raise to the power of .
Step 4.1.2.2
Raise to the power of .
Step 4.1.2.3
Use the power rule to combine exponents.
Step 4.1.2.4
Add and .
Step 4.1.3
Rewrite as .
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Step 4.1.3.1
Use to rewrite as .
Step 4.1.3.2
Apply the power rule and multiply exponents, .
Step 4.1.3.3
Combine and .
Step 4.1.3.4
Cancel the common factor of .
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Step 4.1.3.4.1
Cancel the common factor.
Step 4.1.3.4.2
Rewrite the expression.
Step 4.1.3.5
Evaluate the exponent.
Step 4.1.4
Multiply by .
Step 4.1.5
Multiply .
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Step 4.1.5.1
Multiply by .
Step 4.1.5.2
Multiply by .
Step 4.2
Add and .
Step 4.3
Subtract from .
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
Multiply by .
Step 6.1.2
Multiply .
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Step 6.1.2.1
Raise to the power of .
Step 6.1.2.2
Raise to the power of .
Step 6.1.2.3
Use the power rule to combine exponents.
Step 6.1.2.4
Add and .
Step 6.1.3
Rewrite as .
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Step 6.1.3.1
Use to rewrite as .
Step 6.1.3.2
Apply the power rule and multiply exponents, .
Step 6.1.3.3
Combine and .
Step 6.1.3.4
Cancel the common factor of .
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Step 6.1.3.4.1
Cancel the common factor.
Step 6.1.3.4.2
Rewrite the expression.
Step 6.1.3.5
Evaluate the exponent.
Step 6.1.4
Multiply by .
Step 6.1.5
Multiply by .
Step 6.2
Subtract from .
Step 6.3
Add and .
Step 7
Multiply by .
Step 8
Combine fractions.
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Step 8.1
Multiply by .
Step 8.2
Expand the denominator using the FOIL method.
Step 8.3
Simplify.
Step 9
Expand using the FOIL Method.
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Step 9.1
Apply the distributive property.
Step 9.2
Apply the distributive property.
Step 9.3
Apply the distributive property.
Step 10
Simplify and combine like terms.
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Step 10.1
Simplify each term.
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Step 10.1.1
Multiply by .
Step 10.1.2
Multiply by .
Step 10.1.3
Multiply by .
Step 10.1.4
Multiply .
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Step 10.1.4.1
Multiply by .
Step 10.1.4.2
Raise to the power of .
Step 10.1.4.3
Raise to the power of .
Step 10.1.4.4
Use the power rule to combine exponents.
Step 10.1.4.5
Add and .
Step 10.1.5
Rewrite as .
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Step 10.1.5.1
Use to rewrite as .
Step 10.1.5.2
Apply the power rule and multiply exponents, .
Step 10.1.5.3
Combine and .
Step 10.1.5.4
Cancel the common factor of .
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Step 10.1.5.4.1
Cancel the common factor.
Step 10.1.5.4.2
Rewrite the expression.
Step 10.1.5.5
Evaluate the exponent.
Step 10.1.6
Multiply by .
Step 10.2
Add and .
Step 10.3
Add and .
Step 11
Cancel the common factor of and .
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Step 11.1
Factor out of .
Step 11.2
Factor out of .
Step 11.3
Factor out of .
Step 11.4
Cancel the common factors.
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Step 11.4.1
Factor out of .
Step 11.4.2
Cancel the common factor.
Step 11.4.3
Rewrite the expression.
Step 11.4.4
Divide by .
Step 12
Expand using the FOIL Method.
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Step 12.1
Apply the distributive property.
Step 12.2
Apply the distributive property.
Step 12.3
Apply the distributive property.
Step 13
Simplify and combine like terms.
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Step 13.1
Simplify each term.
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Step 13.1.1
Multiply by .
Step 13.1.2
Combine using the product rule for radicals.
Step 13.1.3
Multiply by .
Step 13.1.4
Rewrite as .
Step 13.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 13.1.6
Move to the left of .
Step 13.2
Add and .
Step 13.3
Add and .
Step 14
The result can be shown in multiple forms.
Exact Form:
Decimal Form: