# Divide ( square root of 4a^2-4b^2)/( square root of 8a-8b)

4a2-4b28a-8b
Combine 4a2-4b2 and 8a-8b into a single radical.
4a2-4b28a-8b
Factor 4 out of 4a2-4b2.
Factor 4 out of 4a2.
4(a2)-4b28a-8b
Factor 4 out of -4b2.
4(a2)+4(-b2)8a-8b
Factor 4 out of 4(a2)+4(-b2).
4(a2-b2)8a-8b
4(a2-b2)8a-8b
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=b.
4(a+b)(a-b)8a-8b
Factor 8 out of 8a-8b.
Factor 8 out of 8a.
4(a+b)(a-b)8(a)-8b
Factor 8 out of -8b.
4(a+b)(a-b)8(a)+8(-b)
Factor 8 out of 8(a)+8(-b).
4(a+b)(a-b)8(a-b)
4(a+b)(a-b)8(a-b)
Reduce the expression 4(a+b)(a-b)8(a-b) by cancelling the common factors.
Factor 4 out of 4(a+b)(a-b).
4((a+b)(a-b))8(a-b)
Factor 4 out of 8(a-b).
4((a+b)(a-b))4(2(a-b))
Cancel the common factor.
4((a+b)(a-b))4(2(a-b))
Rewrite the expression.
(a+b)(a-b)2(a-b)
(a+b)(a-b)2(a-b)
Reduce the expression (a+b)(a-b)2(a-b) by cancelling the common factors.
Cancel the common factor.
(a+b)(a-b)2(a-b)
Rewrite the expression.
a+b2
a+b2
Rewrite a+b2 as a+b2.
a+b2
Multiply a+b2 by 22.
a+b2⋅22
Combine and simplify the denominator.
Multiply a+b2 and 22.
a+b222
Raise 2 to the power of 1.
a+b2212
Raise 2 to the power of 1.
a+b22121
Use the power rule aman=am+n to combine exponents.
a+b221+1
a+b222
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
a+b2(212)2
Apply the power rule and multiply exponents, (am)n=amn.
a+b2212⋅2
Combine 12 and 2.
a+b2222
Cancel the common factor of 2.
Cancel the common factor.
a+b2222
Divide 1 by 1.
a+b221
a+b221
Evaluate the exponent.
a+b22
a+b22
a+b22
Combine using the product rule for radicals.
(a+b)⋅22
Reorder factors in (a+b)⋅22.
2(a+b)2
Divide ( square root of 4a^2-4b^2)/( square root of 8a-8b)