\(=\dfrac{\sqrt{a}+1}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}-\dfrac{\sqrt{a}-1}{\left(\sqrt{a}+2\right)^2}\left(\dfrac{\sqrt{a}\left(a+2\sqrt{a}-4\right)-2}{\sqrt{a}}\right)\\ =\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\right)-\left[\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)\right]}{\left(\sqrt{a}+2\right)^2\left(\sqrt{a}-2\right)}.\left(a+2\sqrt{a}+1-5\right)-2\\ =\dfrac{a+3\sqrt{a}+2-a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)^2\left(\sqrt{a}-2\right)}\left(\sqrt{a}+2\right)^2-7\)
\(=\dfrac{6\sqrt{a}+4}{\sqrt{a}-2}-7=\dfrac{6\sqrt{a}+4-7\sqrt{a}+14}{\sqrt{a}-2}\\ =\dfrac{-\sqrt{a}+18}{\sqrt{a}-2}\)
\(\left(\dfrac{\sqrt{a}+1}{a-4}-\dfrac{\sqrt{a}-1}{a+4\sqrt{a}+4}\right)\left(\dfrac{a\sqrt{a}+2a-4\sqrt{a}-2}{\sqrt{a}}\right)\)
\(=\left[\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)^2}-\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)^2}\right]\left[\dfrac{a\sqrt{a}+2a-4\sqrt{a}-2}{\sqrt{a}}\right]\)
\(=\dfrac{a+3\sqrt{a}+2-a+3\sqrt{a}+2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)^2}\left[\dfrac{a\sqrt{a}+2a-4\sqrt{a}-2}{\sqrt{a}}\right]\)
\(=\dfrac{6\sqrt{a}+4}{\left(\sqrt{a}-2\right)\left(a+4\sqrt{a}+4\right)}\left(\dfrac{a\sqrt{a}+2a-4\sqrt{a}-2}{\sqrt{a}}\right)\)
\(=\dfrac{6\sqrt{a}+4}{a\sqrt{a}+4a+4\sqrt{a}-2a-8\sqrt{a}-8}\left(\dfrac{a\sqrt{a}+2a-4\sqrt{a}-2}{\sqrt{a}}\right)\)
\(=\dfrac{6\sqrt{a}+4}{a\sqrt{a}+2a-4\sqrt{a}-8}\left(\dfrac{a\sqrt{a}+2a-4\sqrt{a}-8+6}{\sqrt{a}}\right)\)
\(=\dfrac{ }{ }\)\(\dfrac{\left(6\sqrt{a}+4\right)\left(a\sqrt{a}+2a-4\sqrt{a}-8\right)}{\left(a\sqrt{a}+2a-4\sqrt{a}-8\right)\sqrt{a}}+\dfrac{\left(6\sqrt{a}+4\right).6}{\left(a\sqrt{a}+2a-4\sqrt{a}-8\right)\sqrt{a}}\)
\(=\dfrac{6\sqrt{a}+4}{\sqrt{a}}+\dfrac{36\sqrt{a}+24}{\sqrt{a}\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)^2}\)??????
=⎡⎣(√a+1)(√a+2)(√a−2)(√a+2)2−(√a−1)(√a−2)(√a−2)(√a+2)2⎤⎦[a√a+2a−4√a−2√a]=[(�+1)(�+2)(�−2)(�+2)2−(�−1)(�−2)(�−2)(�+2)2][��+2�−4�−2�]
=6√a+4(√a−2)(a+4√a+4)(a√a+2a−4√a−2√a)=6�+4(�−2)(�+4�+4)(��+2�−4�−2�)
=6√a+4a√a+2a−4√a−8(a√a+2a−4√a−8+6√a)=6�+4��+2�−4�−8(��+2�−4�−8+6�)
(6√a+4)(a√a+2a−4√a−8)(a√a+2a−4√a−8)√a+(6√a+4).6(a√a+2a−4√a−8)√a(6�+4)(��+2�−4�−8)(��+2�−4�−8)�+(6�+4).6(��+2�−4�−8)�
