# Simplify ( square root of a- square root of b)/( square root of a+ square root of b)+(a+2 square root of ab+b)/(a-b)

a-ba+b+a+2ab+ba-b
Simplify terms.
Simplify each term.
Multiply a-ba+b by a-ba-b.
a-ba+b⋅a-ba-b+a+2ab+ba-b
Multiply a-ba+b and a-ba-b.
(a-b)(a-b)(a+b)(a-b)+a+2ab+ba-b
Expand the denominator using the FOIL method.
(a-b)(a-b)a2-ab+ba-b2+a+2ab+ba-b
Simplify.
(a-b)(a-b)a-b+a+2ab+ba-b
Simplify the numerator.
Raise a-b to the power of 1.
(a-b)1(a-b)a-b+a+2ab+ba-b
Raise a-b to the power of 1.
(a-b)1(a-b)1a-b+a+2ab+ba-b
Use the power rule aman=am+n to combine exponents.
(a-b)1+1a-b+a+2ab+ba-b
(a-b)2a-b+a+2ab+ba-b
(a-b)2a-b+a+2ab+ba-b
Rewrite (a-b)2 as (a-b)(a-b).
(a-b)(a-b)a-b+a+2ab+ba-b
Expand (a-b)(a-b) using the FOIL Method.
Apply the distributive property.
a(a-b)-b(a-b)a-b+a+2ab+ba-b
Apply the distributive property.
aa+a(-b)-b(a-b)a-b+a+2ab+ba-b
Apply the distributive property.
aa+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
aa+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Simplify and combine like terms.
Simplify each term.
Multiply aa.
Raise a to the power of 1.
a1a+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Raise a to the power of 1.
a1a1+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Use the power rule aman=am+n to combine exponents.
a1+1+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
a2+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
a2+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Rewrite a2 as a.
Use axn=axn to rewrite a as a12.
(a12)2+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Apply the power rule and multiply exponents, (am)n=amn.
a12⋅2+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Combine 12 and 2.
a22+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Cancel the common factor of 2.
Cancel the common factor.
a22+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Divide 1 by 1.
a1+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
a1+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Simplify.
a+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
a+a(-b)-ba-b(-b)a-b+a+2ab+ba-b
Rewrite using the commutative property of multiplication.
a-ab-ba-b(-b)a-b+a+2ab+ba-b
Combine using the product rule for radicals.
a-ba-ba-b(-b)a-b+a+2ab+ba-b
Combine using the product rule for radicals.
a-ba-ab-b(-b)a-b+a+2ab+ba-b
Multiply -b(-b).
Multiply -1 by -1.
a-ba-ab+1bba-b+a+2ab+ba-b
Multiply b by 1.
a-ba-ab+bba-b+a+2ab+ba-b
Raise b to the power of 1.
a-ba-ab+b1ba-b+a+2ab+ba-b
Raise b to the power of 1.
a-ba-ab+b1b1a-b+a+2ab+ba-b
Use the power rule aman=am+n to combine exponents.
a-ba-ab+b1+1a-b+a+2ab+ba-b
a-ba-ab+b2a-b+a+2ab+ba-b
a-ba-ab+b2a-b+a+2ab+ba-b
Rewrite b2 as b.
Use axn=axn to rewrite b as b12.
a-ba-ab+(b12)2a-b+a+2ab+ba-b
Apply the power rule and multiply exponents, (am)n=amn.
a-ba-ab+b12⋅2a-b+a+2ab+ba-b
Combine 12 and 2.
a-ba-ab+b22a-b+a+2ab+ba-b
Cancel the common factor of 2.
Cancel the common factor.
a-ba-ab+b22a-b+a+2ab+ba-b
Divide 1 by 1.
a-ba-ab+b1a-b+a+2ab+ba-b
a-ba-ab+b1a-b+a+2ab+ba-b
Simplify.
a-ba-ab+ba-b+a+2ab+ba-b
a-ba-ab+ba-b+a+2ab+ba-b
a-ba-ab+ba-b+a+2ab+ba-b
Subtract ab from -ba.
Reorder b and a.
a-ab-ab+ba-b+a+2ab+ba-b
Subtract ab from -ab.
a-2ab+ba-b+a+2ab+ba-b
a-2ab+ba-b+a+2ab+ba-b
a-2ab+ba-b+a+2ab+ba-b
a-2ab+ba-b+a+2ab+ba-b
Combine the numerators over the common denominator.
a-2ab+b+a+2ab+ba-b
a-2ab+b+a+2ab+ba-b
Simplify the numerator.
2a-2ab+b+2ab+ba-b
2a+b+0+ba-b
2a+b+ba-b
2a+2ba-b
Factor 2 out of 2a+2b.
Factor 2 out of 2a.
2(a)+2ba-b
Factor 2 out of 2b.
2(a)+2(b)a-b
Factor 2 out of 2(a)+2(b).
2(a+b)a-b
2(a+b)a-b
2(a+b)a-b
Simplify ( square root of a- square root of b)/( square root of a+ square root of b)+(a+2 square root of ab+b)/(a-b)