Question

Đề: Rút gọn biểu thức

Answer 1

\(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}=\dfrac{x-1}{\sqrt{y}-1}\dfrac{\sqrt{\left(\sqrt{y}-1\right)^4}}{\left(x-1\right)^2}=\dfrac{x-1}{\sqrt{y}-1}.\dfrac{\left(\sqrt{y}-1\right)^2}{\left(x-1\right)^2}=\dfrac{\sqrt{y}-1}{x-1}\)

Answer 2

b: Ta có: \(\dfrac{x-1}{\sqrt{y}-1}\cdot\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\)

\(=\dfrac{x-1}{\sqrt{y}-1}\cdot\dfrac{\left(\sqrt{y}-1\right)^2}{\left(x-1\right)^2}\)

\(=\dfrac{\sqrt{y}-1}{x-1}\)