Factor ( square root of a)/( square root of a- square root of b)-( square root of b)/( square root of a+ square root of b)

Math
aa-b-ba+b
Multiply ba+b by a-ba-b.
aa-b-(ba+b⋅a-ba-b)
Multiply ba+b and a-ba-b.
aa-b-b(a-b)(a+b)(a-b)
Expand the denominator using the FOIL method.
aa-b-b(a-b)a2-ab+ba-b2
Simplify.
aa-b-b(a-b)a-b
Apply the distributive property.
aa-b-ba+b(-b)a-b
Combine using the product rule for radicals.
aa-b-ba+b(-b)a-b
Rewrite using the commutative property of multiplication.
aa-b-ba-bba-b
Simplify each term.
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Multiply -bb.
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Raise b to the power of 1.
aa-b-ba-(b1b)a-b
Raise b to the power of 1.
aa-b-ba-(b1b1)a-b
Use the power rule aman=am+n to combine exponents.
aa-b-ba-b1+1a-b
Add 1 and 1.
aa-b-ba-b2a-b
aa-b-ba-b2a-b
Rewrite b2 as b.
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Use axn=axn to rewrite b as b12.
aa-b-ba-(b12)2a-b
Apply the power rule and multiply exponents, (am)n=amn.
aa-b-ba-b12⋅2a-b
Combine 12 and 2.
aa-b-ba-b22a-b
Cancel the common factor of 2.
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Cancel the common factor.
aa-b-ba-b22a-b
Rewrite the expression.
aa-b-ba-b1a-b
aa-b-ba-b1a-b
Simplify.
aa-b-ba-ba-b
aa-b-ba-ba-b
aa-b-ba-ba-b
Simplify the numerator.
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Use axn=axn to rewrite ba as (ba)12.
aa-b-(ba)12-ba-b
Apply the product rule to ba.
aa-b-b12a12-ba-b
Factor b12 out of b12a12-b.
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Reorder b12 and a12.
aa-b-a12b12-ba-b
Factor b12 out of a12b12.
aa-b-b12a12-ba-b
Factor b12 out of -b.
aa-b-b12a12+b12(-b12)a-b
Factor b12 out of b12a12+b12(-b12).
aa-b-b12(a12-b12)a-b
aa-b-b12(a12-b12)a-b
aa-b-b12(a12-b12)a-b
To write aa-b as a fraction with a common denominator, multiply by a-ba-b.
aa-b⋅a-ba-b-b12(a12-b12)a-b
To write -b12(a12-b12)a-b as a fraction with a common denominator, multiply by a-ba-b.
aa-b⋅a-ba-b-b12(a12-b12)a-b⋅a-ba-b
Write each expression with a common denominator of a-b(a-b), by multiplying each by an appropriate factor of 1.
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Multiply aa-b and a-ba-b.
a(a-b)a-b(a-b)-b12(a12-b12)a-b⋅a-ba-b
Multiply b12(a12-b12)a-b and a-ba-b.
a(a-b)a-b(a-b)-b12(a12-b12)a-b(a-b)a-b
Reorder the factors of (a-b)a-b.
a(a-b)a-b(a-b)-b12(a12-b12)a-ba-b(a-b)
a(a-b)a-b(a-b)-b12(a12-b12)a-ba-b(a-b)
Combine the numerators over the common denominator.
a(a-b)-b12(a12-b12)a-ba-b(a-b)
Rewrite a(a-b)-b12(a12-b12)a-ba-b(a-b) in a factored form.
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Apply the distributive property.
aa+a(-b)-b12(a12-b12)a-ba-b(a-b)
Rewrite using the commutative property of multiplication.
aa-ab-b12(a12-b12)a-ba-b(a-b)
Apply the distributive property.
aa-ab+(-b12a12-b12(-b12))a-ba-b(a-b)
Rewrite using the commutative property of multiplication.
aa-ab+(-b12a12-1⋅-1b12b12)a-ba-b(a-b)
Simplify each term.
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Multiply b12 by b12 by adding the exponents.
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Move b12.
aa-ab+(-b12a12-1⋅-1(b12b12))a-ba-b(a-b)
Use the power rule aman=am+n to combine exponents.
aa-ab+(-b12a12-1⋅-1b12+12)a-ba-b(a-b)
Combine the numerators over the common denominator.
aa-ab+(-b12a12-1⋅-1b1+12)a-ba-b(a-b)
Add 1 and 1.
aa-ab+(-b12a12-1⋅-1b22)a-ba-b(a-b)
Divide 2 by 2.
aa-ab+(-b12a12-1⋅-1b1)a-ba-b(a-b)
aa-ab+(-b12a12-1⋅-1b1)a-ba-b(a-b)
Simplify -1⋅-1b1.
aa-ab+(-b12a12-1⋅-1b)a-ba-b(a-b)
Multiply -1 by -1.
aa-ab+(-b12a12+1b)a-ba-b(a-b)
Multiply b by 1.
aa-ab+(-b12a12+b)a-ba-b(a-b)
aa-ab+(-b12a12+b)a-ba-b(a-b)
Apply the distributive property.
aa-ab-b12a12a-b+ba-ba-b(a-b)
aa-ab-b12a12a-b+ba-ba-b(a-b)
Factor ( square root of a)/( square root of a- square root of b)-( square root of b)/( square root of a+ square root of b)

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