Algebra Examples

Simplify ( square root of x+ square root of y)/( square root of x- square root of y)
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.
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Step 2.3.1
Rewrite as .
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Step 2.3.1.1
Use to rewrite as .
Step 2.3.1.2
Apply the power rule and multiply exponents, .
Step 2.3.1.3
Combine and .
Step 2.3.1.4
Cancel the common factor of .
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Step 2.3.1.4.1
Cancel the common factor.
Step 2.3.1.4.2
Rewrite the expression.
Step 2.3.1.5
Simplify.
Step 2.3.2
Rewrite as .
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Step 2.3.2.1
Use to rewrite as .
Step 2.3.2.2
Apply the power rule and multiply exponents, .
Step 2.3.2.3
Combine and .
Step 2.3.2.4
Cancel the common factor of .
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Step 2.3.2.4.1
Cancel the common factor.
Step 2.3.2.4.2
Rewrite the expression.
Step 2.3.2.5
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
Multiply .
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Step 6.1.1.1
Raise to the power of .
Step 6.1.1.2
Raise to the power of .
Step 6.1.1.3
Use the power rule to combine exponents.
Step 6.1.1.4
Add and .
Step 6.1.2
Rewrite as .
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Step 6.1.2.1
Use to rewrite as .
Step 6.1.2.2
Apply the power rule and multiply exponents, .
Step 6.1.2.3
Combine and .
Step 6.1.2.4
Cancel the common factor of .
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Step 6.1.2.4.1
Cancel the common factor.
Step 6.1.2.4.2
Rewrite the expression.
Step 6.1.2.5
Simplify.
Step 6.1.3
Combine using the product rule for radicals.
Step 6.1.4
Combine using the product rule for radicals.
Step 6.1.5
Multiply .
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Step 6.1.5.1
Raise to the power of .
Step 6.1.5.2
Raise to the power of .
Step 6.1.5.3
Use the power rule to combine exponents.
Step 6.1.5.4
Add and .
Step 6.1.6
Rewrite as .
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Step 6.1.6.1
Use to rewrite as .
Step 6.1.6.2
Apply the power rule and multiply exponents, .
Step 6.1.6.3
Combine and .
Step 6.1.6.4
Cancel the common factor of .
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Step 6.1.6.4.1
Cancel the common factor.
Step 6.1.6.4.2
Rewrite the expression.
Step 6.1.6.5
Simplify.
Step 6.2
Add and .
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Step 6.2.1
Reorder and .
Step 6.2.2
Add and .