\(\sqrt{(a+b)^{-1}}\times\sqrt{(a-b)(a^2-b^2)}\)
= \(\sqrt{(a+b)^{-1}(a-b)(a+b)(a-b)}\)
= \(\sqrt{(a+b)^{-1+1}(a-b)^2}\)
=\(\sqrt{(a+b)^0(a-b)^2}\)
= \(\sqrt{1.(a-b)^2}\)
= (a - b)
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Simplify: \(\sqrt{(a+b)^{-1}}\times\sqrt{(a-b)(a^2-b^2)}\)
\(\sqrt{(a+b)^{-1}}\times\sqrt{(a-b)(a^2-b^2)}\)
= \(\sqrt{(a+b)^{-1}(a-b)(a+b)(a-b)}\)
= \(\sqrt{(a+b)^{-1+1}(a-b)^2}\)
=\(\sqrt{(a+b)^0(a-b)^2}\)
= \(\sqrt{1.(a-b)^2}\)
= (a - b)
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