Basic Math Examples

Multiply (( square root of b)/(a- square root of ab)-( square root of a)/( square root of ab-b))(a square root of b-b square root of a)
Step 1
Simplify each term.
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Step 1.1
Simplify the denominator.
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Step 1.1.1
Use to rewrite as .
Step 1.1.2
Apply the product rule to .
Step 1.1.3
Rewrite in a factored form.
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Step 1.1.3.1
Factor out of .
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Step 1.1.3.1.1
Raise to the power of .
Step 1.1.3.1.2
Factor out of .
Step 1.1.3.1.3
Factor out of .
Step 1.1.3.1.4
Factor out of .
Step 1.1.3.2
Rewrite as .
Step 1.2
Simplify the denominator.
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Step 1.2.1
Use to rewrite as .
Step 1.2.2
Apply the product rule to .
Step 1.2.3
Factor out of .
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Step 1.2.3.1
Factor out of .
Step 1.2.3.2
Factor out of .
Step 1.2.3.3
Factor out of .
Step 2
Expand using the FOIL Method.
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Step 2.1
Apply the distributive property.
Step 2.2
Apply the distributive property.
Step 2.3
Apply the distributive property.
Step 3
Simplify and combine like terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Multiply .
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Step 3.1.1.1
Combine and .
Step 3.1.1.2
Combine and .
Step 3.1.1.3
Raise to the power of .
Step 3.1.1.4
Raise to the power of .
Step 3.1.1.5
Use the power rule to combine exponents.
Step 3.1.1.6
Add and .
Step 3.1.2
Move to the numerator using the negative exponent rule .
Step 3.1.3
Multiply by by adding the exponents.
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Step 3.1.3.1
Move .
Step 3.1.3.2
Multiply by .
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Step 3.1.3.2.1
Raise to the power of .
Step 3.1.3.2.2
Use the power rule to combine exponents.
Step 3.1.3.3
Write as a fraction with a common denominator.
Step 3.1.3.4
Combine the numerators over the common denominator.
Step 3.1.3.5
Add and .
Step 3.1.4
Rewrite as .
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Step 3.1.4.1
Use to rewrite as .
Step 3.1.4.2
Apply the power rule and multiply exponents, .
Step 3.1.4.3
Combine and .
Step 3.1.4.4
Cancel the common factor of .
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Step 3.1.4.4.1
Cancel the common factor.
Step 3.1.4.4.2
Rewrite the expression.
Step 3.1.4.5
Simplify.
Step 3.1.5
Rewrite using the commutative property of multiplication.
Step 3.1.6
Multiply .
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Step 3.1.6.1
Combine and .
Step 3.1.6.2
Combine and .
Step 3.1.6.3
Combine using the product rule for radicals.
Step 3.1.7
Multiply .
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Step 3.1.7.1
Combine and .
Step 3.1.7.2
Combine and .
Step 3.1.7.3
Combine using the product rule for radicals.
Step 3.1.8
Multiply .
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Step 3.1.8.1
Multiply by .
Step 3.1.8.2
Multiply by .
Step 3.1.8.3
Combine and .
Step 3.1.8.4
Combine and .
Step 3.1.8.5
Raise to the power of .
Step 3.1.8.6
Raise to the power of .
Step 3.1.8.7
Use the power rule to combine exponents.
Step 3.1.8.8
Add and .
Step 3.1.9
Move to the numerator using the negative exponent rule .
Step 3.1.10
Multiply by by adding the exponents.
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Step 3.1.10.1
Move .
Step 3.1.10.2
Multiply by .
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Step 3.1.10.2.1
Raise to the power of .
Step 3.1.10.2.2
Use the power rule to combine exponents.
Step 3.1.10.3
Write as a fraction with a common denominator.
Step 3.1.10.4
Combine the numerators over the common denominator.
Step 3.1.10.5
Add and .
Step 3.1.11
Rewrite as .
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Step 3.1.11.1
Use to rewrite as .
Step 3.1.11.2
Apply the power rule and multiply exponents, .
Step 3.1.11.3
Combine and .
Step 3.1.11.4
Cancel the common factor of .
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Step 3.1.11.4.1
Cancel the common factor.
Step 3.1.11.4.2
Rewrite the expression.
Step 3.1.11.5
Simplify.
Step 3.2
To write as a fraction with a common denominator, multiply by .
Step 3.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.3.1
Multiply by .
Step 3.3.2
Reorder the factors of .
Step 3.4
Combine the numerators over the common denominator.
Step 3.5
To write as a fraction with a common denominator, multiply by .
Step 3.6
To write as a fraction with a common denominator, multiply by .
Step 3.7
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 3.7.3
Reorder the factors of .
Step 3.7.4
Reorder the factors of .
Step 3.8
Combine the numerators over the common denominator.
Step 3.9
To write as a fraction with a common denominator, multiply by .
Step 3.10
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.10.1
Multiply by .
Step 3.10.2
Reorder the factors of .
Step 3.11
Combine the numerators over the common denominator.
Step 4
Simplify the numerator.
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Step 4.1
Use to rewrite as .
Step 4.2
Use to rewrite as .
Step 4.3
Simplify each term.
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Step 4.3.1
Multiply by by adding the exponents.
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Step 4.3.1.1
Move .
Step 4.3.1.2
Use the power rule to combine exponents.
Step 4.3.1.3
Combine the numerators over the common denominator.
Step 4.3.1.4
Add and .
Step 4.3.1.5
Divide by .
Step 4.3.2
Simplify .
Step 4.3.3
Apply the product rule to .
Step 4.3.4
Multiply by by adding the exponents.
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Step 4.3.4.1
Move .
Step 4.3.4.2
Multiply by .
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Step 4.3.4.2.1
Raise to the power of .
Step 4.3.4.2.2
Use the power rule to combine exponents.
Step 4.3.4.3
Write as a fraction with a common denominator.
Step 4.3.4.4
Combine the numerators over the common denominator.
Step 4.3.4.5
Add and .
Step 4.4
Apply the distributive property.
Step 4.5
Multiply by by adding the exponents.
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Step 4.5.1
Move .
Step 4.5.2
Multiply by .
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Step 4.5.2.1
Raise to the power of .
Step 4.5.2.2
Use the power rule to combine exponents.
Step 4.5.3
Write as a fraction with a common denominator.
Step 4.5.4
Combine the numerators over the common denominator.
Step 4.5.5
Add and .
Step 4.6
Multiply by by adding the exponents.
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Step 4.6.1
Move .
Step 4.6.2
Use the power rule to combine exponents.
Step 4.6.3
Combine the numerators over the common denominator.
Step 4.6.4
Add and .
Step 4.6.5
Divide by .
Step 4.7
Multiply by by adding the exponents.
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Step 4.7.1
Move .
Step 4.7.2
Multiply by .
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Step 4.7.2.1
Raise to the power of .
Step 4.7.2.2
Use the power rule to combine exponents.
Step 4.7.3
Write as a fraction with a common denominator.
Step 4.7.4
Combine the numerators over the common denominator.
Step 4.7.5
Add and .
Step 4.8
Apply the product rule to .
Step 4.9
Multiply by by adding the exponents.
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Step 4.9.1
Move .
Step 4.9.2
Use the power rule to combine exponents.
Step 4.9.3
Combine the numerators over the common denominator.
Step 4.9.4
Add and .
Step 4.9.5
Divide by .
Step 4.10
Multiply by by adding the exponents.
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Step 4.10.1
Move .
Step 4.10.2
Use the power rule to combine exponents.
Step 4.10.3
Combine the numerators over the common denominator.
Step 4.10.4
Add and .
Step 4.10.5
Divide by .
Step 4.11
Simplify .
Step 4.12
Multiply by by adding the exponents.
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Step 4.12.1
Move .
Step 4.12.2
Multiply by .
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Step 4.12.2.1
Raise to the power of .
Step 4.12.2.2
Use the power rule to combine exponents.
Step 4.12.3
Write as a fraction with a common denominator.
Step 4.12.4
Combine the numerators over the common denominator.
Step 4.12.5
Add and .
Step 4.13
Rewrite in a factored form.
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Step 4.13.1
Factor out of .
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Step 4.13.1.1
Reorder the expression.
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Step 4.13.1.1.1
Move .
Step 4.13.1.1.2
Reorder and .
Step 4.13.1.2
Factor out of .
Step 4.13.1.3
Factor out of .
Step 4.13.1.4
Factor out of .
Step 4.13.1.5
Factor out of .
Step 4.13.1.6
Factor out of .
Step 4.13.1.7
Factor out of .
Step 4.13.1.8
Factor out of .
Step 4.13.2
Regroup terms.
Step 4.13.3
Factor out of .
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Step 4.13.3.1
Factor out of .
Step 4.13.3.2
Factor out of .
Step 4.13.3.3
Factor out of .
Step 4.13.4
Factor out of .
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Step 4.13.4.1
Factor out of .
Step 4.13.4.2
Factor out of .
Step 4.13.4.3
Factor out of .
Step 4.13.5
Rewrite as .
Step 4.13.6
Rewrite as .
Step 4.13.7
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Step 4.13.8
Simplify.
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Step 4.13.8.1
Multiply the exponents in .
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Step 4.13.8.1.1
Apply the power rule and multiply exponents, .
Step 4.13.8.1.2
Cancel the common factor of .
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Step 4.13.8.1.2.1
Cancel the common factor.
Step 4.13.8.1.2.2
Rewrite the expression.
Step 4.13.8.2
Simplify.
Step 4.13.8.3
Multiply the exponents in .
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Step 4.13.8.3.1
Apply the power rule and multiply exponents, .
Step 4.13.8.3.2
Cancel the common factor of .
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Step 4.13.8.3.2.1
Cancel the common factor.
Step 4.13.8.3.2.2
Rewrite the expression.
Step 4.13.8.4
Simplify.
Step 4.13.9
Factor out of .
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Step 4.13.9.1
Reorder the expression.
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Step 4.13.9.1.1
Move .
Step 4.13.9.1.2
Move .
Step 4.13.9.1.3
Reorder and .
Step 4.13.9.2
Factor out of .
Step 4.13.9.3
Factor out of .
Step 4.13.9.4
Factor out of .
Step 4.13.10
Rewrite as .
Step 4.13.11
Apply the distributive property.
Step 4.13.12
Simplify.
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Step 4.13.12.1
Rewrite as .
Step 4.13.12.2
Rewrite as .
Step 4.13.12.3
Multiply .
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Step 4.13.12.3.1
Multiply by .
Step 4.13.12.3.2
Multiply by .
Step 4.13.13
Add and .
Step 5
Simplify terms.
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Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 5.3
Cancel the common factor.
Step 5.4
Rewrite the expression.
Step 5.5
Factor out of .
Step 5.6
Factor out of .
Step 5.7
Factor out of .
Step 5.8
Factor out of .
Step 5.9
Factor out of .
Step 5.10
Simplify the expression.
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Step 5.10.1
Rewrite as .
Step 5.10.2
Move the negative in front of the fraction.