Simplify 1/( square root of a- square root of b)

Math
1a-b
Multiply 1a-b by a+ba+b.
1a-b⋅a+ba+b
Multiply 1a-b and a+ba+b.
a+b(a-b)(a+b)
Expand the denominator using the FOIL method.
a+ba2+ab-ab-b2
Simplify.
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Rewrite a2 as a.
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Use axn=axn to rewrite a as a12.
a+b(a12)2-b2
Apply the power rule and multiply exponents, (am)n=amn.
a+ba12⋅2-b2
Combine 12 and 2.
a+ba22-b2
Cancel the common factor of 2.
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Cancel the common factor.
a+ba22-b2
Divide 1 by 1.
a+ba1-b2
a+ba1-b2
Simplify.
a+ba-b2
a+ba-b2
Rewrite b2 as b.
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Use axn=axn to rewrite b as b12.
a+ba-(b12)2
Apply the power rule and multiply exponents, (am)n=amn.
a+ba-b12⋅2
Combine 12 and 2.
a+ba-b22
Cancel the common factor of 2.
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Cancel the common factor.
a+ba-b22
Divide 1 by 1.
a+ba-b1
a+ba-b1
Simplify.
a+ba-b
a+ba-b
a+ba-b
Simplify 1/( square root of a- square root of b)

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