Question

[Ngọc Trâm Tăng]

Rút gọn biểu thức :

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

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

c) \(\dfrac{a\sqrt{a}-8+2a-4\sqrt{a}}{a-4}\)

d) \(\dfrac{1}{2a-1}\) . \(\sqrt{5a^4\left(1-4a+4a^2\right)}\) ( a>\(\dfrac{1}{2}\))

Thanks mấy man trước nkoa 😊😊 😘😍

Answer 1

[Mysterious Person]

a) \(\dfrac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}:\dfrac{1}{\sqrt{a}-\sqrt{b}}=\dfrac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}:\dfrac{1}{\sqrt{a}-\sqrt{b}}\)

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

b) đề sai rồi nha

c) \(\dfrac{a\sqrt{a}-8+2a-4\sqrt{a}}{a-4}=\dfrac{a\sqrt{a}-4\sqrt{a}+2a-8}{a-4}\)

\(=\dfrac{\sqrt{a}\left(a-4\right)+2\left(a-4\right)}{a-4}=\dfrac{\left(\sqrt{a}+2\right)\left(a-4\right)}{a-4}=\sqrt{a}+2\)