Đáp án+giải thích các bước giải:

a)

$(\sqrt{75}+\sqrt{12}-\sqrt{5}).\sqrt{5}-2\sqrt{15}$

$=(\sqrt{5^2.3}+\sqrt{2^2}{3}-\sqrt{5}).\sqrt{5}-2\sqrt{15}$

$=(5\sqrt{3}+2\sqrt{3}-\sqrt{5}).\sqrt{5}-2\sqrt{15}$

$=5\sqrt{15}+2\sqrt{15}-5-2\sqrt{15}$

$=5\sqrt{15}-5$

b)

$(\dfrac{1}{a+\sqrt{a}}+\dfrac{1}{\sqrt{a}+1}):\dfrac{a-\sqrt{a}+1}{a\sqrt{a}+1}$ (a>0)

$=(\dfrac{1}{\sqrt{a}(\sqrt{a}+1)}+\dfrac{1.\sqrt{a}}{\sqrt{a}(\sqrt{a}+1)}):\dfrac{a-\sqrt{a}+1}{a\sqrt{a}+1}$ 

$=\dfrac{1+\sqrt{a}}{\sqrt{a}(\sqrt{a}+1)}:\dfrac{a-\sqrt{a}+1}{(\sqrt{a}+1)(a-\sqrt{a}+1)}$ 

$=\dfrac{1+\sqrt{a}}{\sqrt{a}(\sqrt{a}+1)}.\dfrac{a\sqrt{a}+1}{\sqrt{a}+1)(a-\sqrt{a}+1)}$

$=\dfrac{(1+\sqrt{a})(\sqrt{a}+1)(a-\sqrt{a}+1)}{\sqrt{a}(\sqrt{a}+1)(\sqrt{a}+1)(a-\sqrt{a}+1)}$

$=\dfrac{1+\sqrt{a}}{\sqrt{a}}$

Đáp án+Giải thích các bước giải:

 a, ($\sqrt{75}$ + $\sqrt{12}$ - $\sqrt{5}$).$\sqrt{5}$ - 2$\sqrt{15}$

=  $\sqrt{75.5}$ + $\sqrt{12.5}$ - $\sqrt{5.5}$ - 2$\sqrt{15}$

= $\sqrt{25.15}$ + $\sqrt{4.15}$ - $\sqrt{25}$ - 2$\sqrt{15}$

= 5$\sqrt{15}$ + 2$\sqrt{15}$ - 5 - 2$\sqrt{15}$

= 5$\sqrt{15}$ - 5

b, ($\dfrac{1}{a + \sqrt{a}}$ + $\dfrac{1}{\sqrt{a} + 1}$) : $\dfrac{a - \sqrt{a} + 1}{a\sqrt{a} + 1}$

= ($\dfrac{1}{\sqrt{a}.(\sqrt{a} + 1)}$ + $\dfrac{1}{\sqrt{a} + 1}$) : $\dfrac{a - \sqrt{a} + 1}{(\sqrt{a} + 1).(a - \sqrt{a} + 1)}$

= $\dfrac{1 + \sqrt{a}}{(\sqrt{a}.(\sqrt{a} + 1)}$ : $\dfrac{1}{\sqrt{a} + 1}$

= $\dfrac{1}{\sqrt{a}}$ .  ($\sqrt{a}$ + 1)

= $\dfrac{\sqrt{a} + 1}{\sqrt{a}}$