Question

Rút bọn biểu thức:

\(\left(\dfrac{\sqrt{x}}{\sqrt{x-2}}+\dfrac{4\sqrt{x}-3}{2\sqrt{x}-1}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}}-\dfrac{\sqrt{x}-4}{\sqrt{x}-2}\right)\)

Answer 1

\(=\dfrac{2\sqrt{x}-\sqrt{x}+4x-8\sqrt{x}-3\sqrt{x}+6}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}:\dfrac{x-4-x+4\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

\(=\dfrac{4x-10\sqrt{x}+6}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{4\left(\sqrt{x}-1\right)}\)

\(=\dfrac{\left(\sqrt{x}-1\right)\left(4\sqrt{x}-6\right)}{\left(2\sqrt{x}-1\right)\cdot4\cdot\left(\sqrt{x}-1\right)}\cdot\sqrt{x}\)

\(=\dfrac{\sqrt{x}\left(2\sqrt{x}-3\right)}{2\left(2\sqrt{x}-1\right)}\)