# 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)

(ba-ab-aab-b)(ab-ba)
Simplify each term.
Multiply ba-ab by a+aba+ab.
(ba-ab⋅a+aba+ab-aab-b)(ab-ba)
Multiply ba-ab and a+aba+ab.
(b(a+ab)(a-ab)(a+ab)-aab-b)(ab-ba)
Expand the denominator using the FOIL method.
(b(a+ab)a2+aab-aba-ab2-aab-b)(ab-ba)
Simplify.
Use axn=axn to rewrite ab as (ab)12.
(b(a+ab)a2-((ab)12)2-aab-b)(ab-ba)
Apply the power rule and multiply exponents, (am)n=amn.
(b(a+ab)a2-(ab)12⋅2-aab-b)(ab-ba)
Combine 12 and 2.
(b(a+ab)a2-(ab)22-aab-b)(ab-ba)
Cancel the common factor of 2.
Cancel the common factor.
(b(a+ab)a2-(ab)22-aab-b)(ab-ba)
Divide 1 by 1.
(b(a+ab)a2-(ab)1-aab-b)(ab-ba)
(b(a+ab)a2-(ab)1-aab-b)(ab-ba)
Simplify.
(b(a+ab)a2-(ab)-aab-b)(ab-ba)
(b(a+ab)a2-ab-aab-b)(ab-ba)
Factor a out of a2-ab.
Factor a out of a2.
(b(a+ab)a⋅a-ab-aab-b)(ab-ba)
Factor a out of -ab.
(b(a+ab)a⋅a+a(-b)-aab-b)(ab-ba)
Factor a out of a⋅a+a(-b).
(b(a+ab)a(a-b)-aab-b)(ab-ba)
(b(a+ab)a(a-b)-aab-b)(ab-ba)
Apply the distributive property.
(ba+baba(a-b)-aab-b)(ab-ba)
Multiply bab.
Combine using the product rule for radicals.
(ba+b(ab)a(a-b)-aab-b)(ab-ba)
Raise b to the power of 1.
(ba+a(b1b)a(a-b)-aab-b)(ab-ba)
Raise b to the power of 1.
(ba+a(b1b1)a(a-b)-aab-b)(ab-ba)
Use the power rule aman=am+n to combine exponents.
(ba+ab1+1a(a-b)-aab-b)(ab-ba)
(ba+ab2a(a-b)-aab-b)(ab-ba)
(ba+ab2a(a-b)-aab-b)(ab-ba)
Simplify each term.
Reorder a and b2.
(ba+b2aa(a-b)-aab-b)(ab-ba)
Pull terms out from under the radical.
(ba+baa(a-b)-aab-b)(ab-ba)
(ba+baa(a-b)-aab-b)(ab-ba)
Multiply aab-b by ab+bab+b.
(ba+baa(a-b)-(aab-b⋅ab+bab+b))(ab-ba)
Multiply aab-b and ab+bab+b.
(ba+baa(a-b)-a(ab+b)(ab-b)(ab+b))(ab-ba)
Expand the denominator using the FOIL method.
(ba+baa(a-b)-a(ab+b)ab2+abb-bab-b2)(ab-ba)
Simplify.
Use axn=axn to rewrite ab as (ab)12.
(ba+baa(a-b)-a(ab+b)((ab)12)2-b2)(ab-ba)
Apply the power rule and multiply exponents, (am)n=amn.
(ba+baa(a-b)-a(ab+b)(ab)12⋅2-b2)(ab-ba)
Combine 12 and 2.
(ba+baa(a-b)-a(ab+b)(ab)22-b2)(ab-ba)
Cancel the common factor of 2.
Cancel the common factor.
(ba+baa(a-b)-a(ab+b)(ab)22-b2)(ab-ba)
Divide 1 by 1.
(ba+baa(a-b)-a(ab+b)(ab)1-b2)(ab-ba)
(ba+baa(a-b)-a(ab+b)(ab)1-b2)(ab-ba)
Simplify.
(ba+baa(a-b)-a(ab+b)ab-b2)(ab-ba)
(ba+baa(a-b)-a(ab+b)ab-b2)(ab-ba)
Factor b out of ab-b2.
Factor b out of ab.
(ba+baa(a-b)-a(ab+b)ba-b2)(ab-ba)
Factor b out of -b2.
(ba+baa(a-b)-a(ab+b)ba+b(-b))(ab-ba)
Factor b out of ba+b(-b).
(ba+baa(a-b)-a(ab+b)b(a-b))(ab-ba)
(ba+baa(a-b)-a(ab+b)b(a-b))(ab-ba)
Apply the distributive property.
(ba+baa(a-b)-aab+abb(a-b))(ab-ba)
Multiply aab.
Combine using the product rule for radicals.
(ba+baa(a-b)-a(ab)+abb(a-b))(ab-ba)
Raise a to the power of 1.
(ba+baa(a-b)-a1ab+abb(a-b))(ab-ba)
Raise a to the power of 1.
(ba+baa(a-b)-a1a1b+abb(a-b))(ab-ba)
Use the power rule aman=am+n to combine exponents.
(ba+baa(a-b)-a1+1b+abb(a-b))(ab-ba)
(ba+baa(a-b)-a2b+abb(a-b))(ab-ba)
(ba+baa(a-b)-a2b+abb(a-b))(ab-ba)
Pull terms out from under the radical.
(ba+baa(a-b)-ab+abb(a-b))(ab-ba)
(ba+baa(a-b)-ab+abb(a-b))(ab-ba)
To write ba+baa(a-b) as a fraction with a common denominator, multiply by bb.
(ba+baa(a-b)⋅bb-ab+abb(a-b))(ab-ba)
To write -ab+abb(a-b) as a fraction with a common denominator, multiply by aa.
(ba+baa(a-b)⋅bb-ab+abb(a-b)⋅aa)(ab-ba)
Write each expression with a common denominator of a(a-b)b, by multiplying each by an appropriate factor of 1.
Multiply ba+baa(a-b) and bb.
((ba+ba)ba(a-b)b-ab+abb(a-b)⋅aa)(ab-ba)
Multiply ab+abb(a-b) and aa.
((ba+ba)ba(a-b)b-(ab+ab)ab(a-b)a)(ab-ba)
Reorder the factors of a(a-b)b.
((ba+ba)bab(a-b)-(ab+ab)ab(a-b)a)(ab-ba)
Reorder the factors of b(a-b)a.
((ba+ba)bab(a-b)-(ab+ab)aab(a-b))(ab-ba)
((ba+ba)bab(a-b)-(ab+ab)aab(a-b))(ab-ba)
Combine the numerators over the common denominator.
(ba+ba)b-(ab+ab)aab(a-b)(ab-ba)
Simplify the numerator.
Apply the distributive property.
bab+bab-(ab+ab)aab(a-b)(ab-ba)
Multiply b by b by adding the exponents.
Move b.
bab+b⋅ba-(ab+ab)aab(a-b)(ab-ba)
Multiply b by b.
bab+b2a-(ab+ab)aab(a-b)(ab-ba)
bab+b2a-(ab+ab)aab(a-b)(ab-ba)
Apply the distributive property.
bab+b2a+(-(ab)-(ab))aab(a-b)(ab-ba)
Apply the distributive property.
bab+b2a-aba-abaab(a-b)(ab-ba)
Multiply a by a by adding the exponents.
Move a.
bab+b2a-(a⋅a)b-abaab(a-b)(ab-ba)
Multiply a by a.
bab+b2a-a2b-abaab(a-b)(ab-ba)
bab+b2a-a2b-abaab(a-b)(ab-ba)
Rewrite bab+b2a-a2b-aba in a factored form.
Regroup terms.
bab-a2b+b2a-abaab(a-b)(ab-ba)
Factor ba out of bab-a2b.
Factor ba out of bab.
ba(b)-a2b+b2a-abaab(a-b)(ab-ba)
Factor ba out of -a2b.
ba(b)+ba(-a)+b2a-abaab(a-b)(ab-ba)
Factor ba out of ba(b)+ba(-a).
ba(b-a)+b2a-abaab(a-b)(ab-ba)
ba(b-a)+b2a-abaab(a-b)(ab-ba)
Factor ba out of b2a-aba.
Factor ba out of b2a.
ba(b-a)+ba(b)-abaab(a-b)(ab-ba)
Factor ba out of -aba.
ba(b-a)+ba(b)+ba(-1a)ab(a-b)(ab-ba)
Factor ba out of ba(b)+ba(-1a).
ba(b-a)+ba(b-1a)ab(a-b)(ab-ba)
ba(b-a)+ba(b-1a)ab(a-b)(ab-ba)
Rewrite -1a as -a.
ba(b-a)+ba(b-a)ab(a-b)(ab-ba)
Factor b-a out of ba(b-a)+ba(b-a).
Factor b-a out of ba(b-a).
(b-a)(ba)+ba(b-a)ab(a-b)(ab-ba)
Factor b-a out of ba(b-a).
(b-a)(ba)+(b-a)(ba)ab(a-b)(ab-ba)
Factor b-a out of (b-a)(ba)+(b-a)(ba).
(b-a)(ba+ba)ab(a-b)(ab-ba)
(b-a)(ba+ba)ab(a-b)(ab-ba)
(b-a)(ba+ba)ab(a-b)(ab-ba)
(b-a)(ba+ba)ab(a-b)(ab-ba)
Simplify terms.
Cancel the common factor of b-a and a-b.
Factor -1 out of b.
(-1(-b)-a)(ba+ba)ab(a-b)(ab-ba)
Factor -1 out of -a.
(-1(-b)-(a))(ba+ba)ab(a-b)(ab-ba)
Factor -1 out of -1(-b)-(a).
-1(-b+a)(ba+ba)ab(a-b)(ab-ba)
Reorder terms.
-1(a-b)(ba+ba)ab(a-b)(ab-ba)
Cancel the common factor.
-1(a-b)(ba+ba)ab(a-b)(ab-ba)
Rewrite the expression.
-1(ba+ba)ab(ab-ba)
-1(ba+ba)ab(ab-ba)
Simplify terms.
Move the negative in front of the fraction.
-ba+baab(ab-ba)
Apply the distributive property.
-ba+baab(ab)-ba+baab(-ba)
Cancel the common factor of a.
Move the leading negative in -ba+baab into the numerator.
-(ba+ba)ab(ab)-ba+baab(-ba)
Factor a out of ab.
-(ba+ba)a(b)(ab)-ba+baab(-ba)
Factor a out of ab.
-(ba+ba)a(b)(a(b))-ba+baab(-ba)
Cancel the common factor.
-(ba+ba)ab(ab)-ba+baab(-ba)
Rewrite the expression.
-(ba+ba)bb-ba+baab(-ba)
-(ba+ba)bb-ba+baab(-ba)
Combine -(ba+ba)b and b.
-(ba+ba)bb-ba+baab(-ba)
Cancel the common factor of b.
Move the leading negative in -ba+baab into the numerator.
-(ba+ba)bb+-(ba+ba)ab(-ba)
Factor b out of ab.
-(ba+ba)bb+-(ba+ba)ba(-ba)
Factor b out of -ba.
-(ba+ba)bb+-(ba+ba)ba(b(-1a))
Cancel the common factor.
-(ba+ba)bb+-(ba+ba)ba(b(-1a))
Rewrite the expression.
-(ba+ba)bb+-(ba+ba)a(-1a)
-(ba+ba)bb+-(ba+ba)a(-1a)
Combine -(ba+ba)a and a.
-(ba+ba)bb-1-(ba+ba)aa
-(ba+ba)bb-1-(ba+ba)aa
Simplify each term.
Group b and ba+ba together.
-(b(ba+ba))b-1-(ba+ba)aa
Apply the distributive property.
-(b(ba)+b(ba))b-1-(ba+ba)aa
Multiply b(ba).
Raise b to the power of 1.
-(b1ba+b(ba))b-1-(ba+ba)aa
Raise b to the power of 1.
-(b1b1a+b(ba))b-1-(ba+ba)aa
Use the power rule aman=am+n to combine exponents.
-(b1+1a+b(ba))b-1-(ba+ba)aa
-(b2a+b(ba))b-1-(ba+ba)aa
-(b2a+b(ba))b-1-(ba+ba)aa
Combine using the product rule for radicals.
-(b2a+bba)b-1-(ba+ba)aa
Rewrite b2 as b.
Use axn=axn to rewrite b as b12.
-((b12)2a+bba)b-1-(ba+ba)aa
Apply the power rule and multiply exponents, (am)n=amn.
-(b12⋅2a+bba)b-1-(ba+ba)aa
Combine 12 and 2.
-(b22a+bba)b-1-(ba+ba)aa
Cancel the common factor of 2.
Cancel the common factor.
-(b22a+bba)b-1-(ba+ba)aa
Divide 1 by 1.
-(b1a+bba)b-1-(ba+ba)aa
-(b1a+bba)b-1-(ba+ba)aa
Simplify.
-(ba+bba)b-1-(ba+ba)aa
-(ba+bba)b-1-(ba+ba)aa
Factor b out of ba+bba.
Factor b out of ba.
-(b(a)+bba)b-1-(ba+ba)aa
Factor b out of bba.
-(b(a)+b(ba))b-1-(ba+ba)aa
Factor b out of b(a)+b(ba).
-(b(a+ba))b-1-(ba+ba)aa
-b(a+ba)b-1-(ba+ba)aa
Cancel the common factor of b.
Cancel the common factor.
-b(a+ba)b-1-(ba+ba)aa
Divide -(a+ba) by 1.
-(a+ba)-1-(ba+ba)aa
-(a+ba)-1-(ba+ba)aa
Apply the distributive property.
-a-ba-1-(ba+ba)aa
Group a and ba+ba together.
-a-ba-1-(a(ba+ba))a
Apply the distributive property.
-a-ba-1-(a(ba)+a(ba))a
Combine using the product rule for radicals.
-a-ba-1-(baa+a(ba))a
Multiply a(ba).
Raise a to the power of 1.
-a-ba-1-(baa+b(a1a))a
Raise a to the power of 1.
-a-ba-1-(baa+b(a1a1))a
Use the power rule aman=am+n to combine exponents.
-a-ba-1-(baa+ba1+1)a
-a-ba-1-(baa+ba2)a
-a-ba-1-(baa+ba2)a
Rewrite a2 as a.
Use axn=axn to rewrite a as a12.
-a-ba-1-(baa+b(a12)2)a
Apply the power rule and multiply exponents, (am)n=amn.
-a-ba-1-(baa+ba12⋅2)a
Combine 12 and 2.
-a-ba-1-(baa+ba22)a
Cancel the common factor of 2.
Cancel the common factor.
-a-ba-1-(baa+ba22)a
Divide 1 by 1.
-a-ba-1-(baa+ba1)a
-a-ba-1-(baa+ba1)a
Simplify.
-a-ba-1-(baa+ba)a
-a-ba-1-(baa+ba)a
Factor a out of baa+ba.
Factor a out of baa.
-a-ba-1-(aba+ba)a
Factor a out of ba.
-a-ba-1-(aba+ab)a
Factor a out of aba+ab.
-a-ba-1-(a(ba+b))a
-a-ba-1-a(ba+b)a
Cancel the common factor of a.
Cancel the common factor.
-a-ba-1-a(ba+b)a
Divide -(ba+b) by 1.
-a-ba-1(-(ba+b))
-a-ba-1(-(ba+b))
Apply the distributive property.
-a-ba-1(-ba-b)
Apply the distributive property.
-a-ba-1(-ba)-1(-b)
Multiply -1(-ba).
Multiply -1 by -1.
-a-ba+1ba-1(-b)
Multiply ba by 1.
-a-ba+ba-1(-b)
-a-ba+ba-1(-b)
Multiply -1(-b).
Multiply -1 by -1.
-a-ba+ba+1b
Multiply b by 1.
-a-ba+ba+b
-a-ba+ba+b
-a-ba+ba+b
Combine the opposite terms in -a-ba+ba+b.