a) \(\left(\frac{\sqrt{a}*\sqrt{a}}{2\sqrt{a}}-\frac{1}{2\sqrt{a}}\right)^2*\left(\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)

= \(\frac{\left(a-1\right)^2}{4a}*\frac{\left(\sqrt{a}-1\right)^2-\left(\sqrt{a}+1\right)^2}{a-1}\) = \(\frac{\left(a-1\right)^2}{4a}*\frac{\left(\sqrt{a}-1-\sqrt{a}-1\right)\left(\sqrt{a}-1+\sqrt{a}+1\right)}{a-1}\)

=\(\frac{\left(a-1\right)^2}{4a}*\frac{-4\sqrt{a}}{a-1}\) = \(\frac{a-1-1}{\sqrt{a}}\) = \(\frac{a-2}{\sqrt{a}}\)

b) P < 0 hay \(\frac{a-2}{\sqrt{a}}\) < 0 . Mà \(\sqrt{a}\) > 0 nên \(a-2\) < 0 . Vậy để P < 0 thì a < 2.

\(2\sqrt4*\sqrt3-\sqrt{16}*\sqrt3+3\sqrt9*\sqrt3-\sqrt{36}*\sqrt3\)

= \(4\sqrt3-4\sqrt3+9\sqrt3-6\sqrt3\)

=\(3\sqrt3\)