Question

H=\(\dfrac{1}{\sqrt{x-1}-\sqrt{x}}+\dfrac{1}{\sqrt{x-1}+\sqrt{x}}+\dfrac{\sqrt{x^3}-x}{\sqrt{x}-1}\) rút gọn BT tren

Answer 1

ĐKXĐ: \(x\ne1\), x > 0

\(H=\dfrac{1}{\sqrt{x-1}-\sqrt{x}}+\dfrac{1}{\sqrt{x-1}+\sqrt{x}}+\dfrac{\sqrt{x^3}-x}{\sqrt{x}-1}\)

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

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

\(=x-2\sqrt{x-1}\)

Answer 2

\(\left\{{}\begin{matrix}x>1\\H=\dfrac{\sqrt{x-1}+\sqrt{x}}{-1}+\dfrac{\sqrt{x-1}-\sqrt{x}}{-1}+x\end{matrix}\right.\)

\(H=x-2\sqrt{x-1}\)