Giải thích các bước giải:
a.Ta có:
$H=(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{2}{a-4})\cdot (\sqrt{a}-1+\dfrac{\sqrt{a}-4}{\sqrt{a}})$
$\to H=(\dfrac{(\sqrt{a}+1)(\sqrt{a}+2)}{(\sqrt{a}+2)(\sqrt{a}-2)}-\dfrac{2}{(\sqrt{a}+2)(\sqrt{a}-2)})\cdot \dfrac{\sqrt{a}(\sqrt{a}-1)+\sqrt{a}-4}{\sqrt{a}}$
$\to H=\dfrac{(\sqrt{a}+1)(\sqrt{a}+2)-2}{(\sqrt{a}+2)(\sqrt{a}-2)}\cdot \dfrac{a-\sqrt{a}+\sqrt{a}-4}{\sqrt{a}}$
$\to H=\dfrac{a+3\sqrt{a}}{a-4}\cdot \dfrac{a-4}{\sqrt{a}}$
$\to H=\dfrac{\sqrt{a}(\sqrt{a}+3)}{a-4}\cdot \dfrac{a-4}{\sqrt{a}}$
$\to H=\sqrt{a}+3$
b.Để $H=a+3$
$\to \sqrt{a}+3=a+3$
$\to \sqrt{a}=a$
$\to a=a^2$
$\to a^2-a=0$
$\to a(a-1)=0$
$\to a=1$ vì $a>0$
