Question

Tìm điều kiện xác định và rút gọn biểu thức:
D=\(\dfrac{\sqrt{x}-2}{\sqrt{x}-3}-\dfrac{5}{x+\sqrt{x}-6}+\dfrac{1}{2-\sqrt{x}}\)

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

Answer 1

a)ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)

Ta có: \(D=\dfrac{\sqrt{x}-2}{\sqrt{x}+3}-\dfrac{5}{x+\sqrt{x}-6}+\dfrac{1}{2-\sqrt{x}}\)

\(=\dfrac{x-4\sqrt{x}+4-5-\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{x-5\sqrt{x}-4}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)