Giải thích các bước giải:
a.Ta có :
$\dfrac{5+3\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}-(\sqrt{5}+3)$
$=\sqrt{5}+3+\dfrac{\sqrt{3}.(\sqrt{3}+1)}{\sqrt{3}+1}-(\sqrt{5}+3)$
$=\sqrt{5}+3+\sqrt{3}-(\sqrt{5}+3)$
$=\sqrt{5}+3+\sqrt{3}-\sqrt{5}-3$
$=\sqrt{3}$
b.Ta có :
$P=a-(\dfrac{1}{\sqrt{a}-\sqrt{a-1}}-\dfrac{1}{\sqrt{a}+\sqrt{a-1}})$
$\rightarrow P=a-(\dfrac{\sqrt{a}+\sqrt{a-1}-(\sqrt{a}-\sqrt{a-1})}{(\sqrt{a}-\sqrt{a-1})(\sqrt{a}+\sqrt{a-1})})$
$\rightarrow P=a-(\dfrac{\sqrt{a}+\sqrt{a-1}-\sqrt{a}+\sqrt{a-1}}{a-(a-1)})$
$\rightarrow P=a-\dfrac{2\sqrt{a-1}}{1}$
$\rightarrow P=a-2\sqrt{a-1}$
$\rightarrow P=a-1-2\sqrt{a-1}+1$
$\rightarrow P=(\sqrt{a-1}-1)^2\ge 0$
