Question

Rút gọn biểu thức :

a) \(\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\) ( a > 0 , b > 0 ) 

b) \(\dfrac{1-8a\sqrt{a}}{1-2\sqrt{a}}\) ( a ≥ 0 , a ≠ \(\dfrac{1}{4}\) ) 

c) \(\dfrac{1-a}{1+\sqrt{a}}\) ( a ≥ 0 )

d) \(\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\) ( a ≥ 0 , a ≠ 9 )

Answer 1

a. \(=\dfrac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}=\sqrt{a}\)

b. \(=\dfrac{1-\left(2\sqrt{a}\right)^3}{1-2\sqrt{a}}=\dfrac{\left(1-2\sqrt{a}\right)\left(1+2\sqrt{a}+4a\right)}{1-2\sqrt{a}}=1+2\sqrt{a}+4a\)

c. \(=\dfrac{1-\left(\sqrt{a}\right)^2}{1+\sqrt{a}}=\dfrac{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)}{1+\sqrt{a}}=1-\sqrt{a}\)

d. \(=\dfrac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}=\sqrt{a}\)