Lời giải:
\(B=\left(\frac{1}{\sqrt{a}(\sqrt{a}-1)}+\frac{1}{\sqrt{a}-1}\right): \frac{\sqrt{a}+1}{a-2\sqrt{a}+1}\)
\(=\left(\frac{1}{\sqrt{a}(\sqrt{a}-1)}+\frac{\sqrt{a}}{\sqrt{a}(\sqrt{a}-1)}\right).\frac{a-2\sqrt{a}+1}{\sqrt{a}+1}\)
\(=\frac{1+\sqrt{a}}{\sqrt{a}(\sqrt{a}-1)}. \frac{(\sqrt{a}-1)^2}{\sqrt{a}+1}\)
\(=\frac{\sqrt{a}-1}{\sqrt{a}}\)