Question

\(\dfrac{1}{\sqrt{x-1}-\sqrt{x}}+\dfrac{1}{\sqrt{x-1}+\sqrt{x}}+\dfrac{\sqrt{x^3}-x}{\sqrt{x-1}}\)giúp mik bài này với mn ơi,mik cảm ơn nhiều lắm!!!!

Answer 1

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

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

\(\Leftrightarrow-\sqrt{x-1}-\sqrt{x}-\sqrt{x-1}+\sqrt{x}+\dfrac{x\sqrt{x}-x}{\sqrt{x-1}}\)

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

\(\Leftrightarrow\dfrac{-2\left(x-1\right)+x\sqrt{x}-x}{\sqrt{x-1}}\)

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

\(\Leftrightarrow\dfrac{-3x+2+x\sqrt{x}}{\sqrt{x-1}}\)

Answer 2

À mình quên ĐKXĐ rồi bạn bổ sung vô nha :v