Question

Rút gọn biểu thức A

A=(\(\dfrac{4\sqrt{y}}{2+\sqrt{y}}+\dfrac{8y}{4-y}\)) : (\(\dfrac{\sqrt{y}-1}{y-2\sqrt{y}}-\dfrac{2}{\sqrt{y}}\))

với y>0; y≠4; y≠9

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 1

\(A=\left(\dfrac{4\sqrt{y}}{2+\sqrt{y}}+\dfrac{8y}{4-y}\right):\left(\dfrac{\sqrt{y}-1}{y-2\sqrt{y}}-\dfrac{2}{\sqrt{y}}\right)\)

\(A=\dfrac{4\sqrt{y}\left(2-\sqrt{y}\right)+8y}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}:\dfrac{\sqrt{y}-1-2\left(\sqrt{y}-2\right)}{\sqrt{y}\left(\sqrt{y}-2\right)}\)

\(A=\dfrac{8\sqrt{y}+4y}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}.\dfrac{\sqrt{y}\left(\sqrt{y}-2\right)}{-\sqrt{y}+3}\)

\(A=\dfrac{4\sqrt{y}}{2-\sqrt{y}}.\dfrac{\sqrt{y}\left(2-\sqrt{y}\right)}{\sqrt{y}-3}\)

\(A=\dfrac{4y}{\sqrt{y}-3}\)

Chúc bạn học tốt ^^