Question

Rút gọn biểu thức:

D = \(\dfrac{1}{\sqrt{h+2\sqrt{h-1}}}+\dfrac{1}{\sqrt{h-2\sqrt{h-1}}}\)

Answer 1

\(A=\dfrac{1}{\sqrt{h+2\sqrt{h-1}}}+\dfrac{1}{\sqrt{h-2\sqrt{h-1}}}\)

\(=\dfrac{1}{\sqrt{\left(\sqrt{h-1}+1\right)^2}}+\dfrac{1}{\sqrt{\left(\sqrt{h-1}-1\right)^2}}\)

\(=\dfrac{1}{\sqrt{h-1}+1}+\dfrac{1}{\left|\sqrt{h-1}-1\right|}\)

 

 

Answer 2

\(D=\dfrac{1}{\sqrt{h+2\sqrt{h-1}}}+\dfrac{1}{\sqrt{h-2\sqrt{h-1}}}\)

\(=\dfrac{1}{\sqrt{h-1}+1}+\dfrac{1}{\sqrt{h-1}-1}\)

\(=\dfrac{2\cdot\sqrt{h-1}}{h}\)