Basic Math Examples

Simplify (1-1/2* square root of 2+1/2* square root of 3)/(1/2* square root of 2)
Step 1
Simplify the numerator.
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Step 1.1
Combine and .
Step 1.2
Combine and .
Step 1.3
Write as a fraction with a common denominator.
Step 1.4
Combine the numerators over the common denominator.
Step 1.5
Combine the numerators over the common denominator.
Step 2
Combine and .
Step 3
Multiply the numerator by the reciprocal of the denominator.
Step 4
Cancel the common factor of .
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Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Multiply by .
Step 6
Combine and simplify the denominator.
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Step 6.1
Multiply by .
Step 6.2
Raise to the power of .
Step 6.3
Raise to the power of .
Step 6.4
Use the power rule to combine exponents.
Step 6.5
Add and .
Step 6.6
Rewrite as .
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Step 6.6.1
Use to rewrite as .
Step 6.6.2
Apply the power rule and multiply exponents, .
Step 6.6.3
Combine and .
Step 6.6.4
Cancel the common factor of .
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Step 6.6.4.1
Cancel the common factor.
Step 6.6.4.2
Rewrite the expression.
Step 6.6.5
Evaluate the exponent.
Step 7
Apply the distributive property.
Step 8
Simplify.
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Step 8.1
Cancel the common factor of .
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Step 8.1.1
Cancel the common factor.
Step 8.1.2
Rewrite the expression.
Step 8.2
Multiply .
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Step 8.2.1
Combine and .
Step 8.2.2
Raise to the power of .
Step 8.2.3
Raise to the power of .
Step 8.2.4
Use the power rule to combine exponents.
Step 8.2.5
Add and .
Step 8.3
Multiply .
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Step 8.3.1
Combine and .
Step 8.3.2
Combine using the product rule for radicals.
Step 8.3.3
Multiply by .
Step 9
Simplify each term.
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Step 9.1
Rewrite as .
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Step 9.1.1
Use to rewrite as .
Step 9.1.2
Apply the power rule and multiply exponents, .
Step 9.1.3
Combine and .
Step 9.1.4
Cancel the common factor of .
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Step 9.1.4.1
Cancel the common factor.
Step 9.1.4.2
Rewrite the expression.
Step 9.1.5
Evaluate the exponent.
Step 9.2
Cancel the common factor of .
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Step 9.2.1
Cancel the common factor.
Step 9.2.2
Rewrite the expression.
Step 9.3
Multiply by .
Step 10
To write as a fraction with a common denominator, multiply by .
Step 11
Combine fractions.
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Step 11.1
Combine and .
Step 11.2
Combine the numerators over the common denominator.
Step 12
Move to the left of .
Step 13
To write as a fraction with a common denominator, multiply by .
Step 14
Combine and .
Step 15
Simplify the expression.
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Step 15.1
Combine the numerators over the common denominator.
Step 15.2
Multiply by .
Step 16
The result can be shown in multiple forms.
Exact Form:
Decimal Form: