Question

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

rút gọn

Answer 1

Lời giải:
ĐKXĐ: \(x>0; x\neq 4\)

Đặt biểu thức đã cho là $P$

\(P=\left[\frac{\sqrt{x}-4}{\sqrt{x}(\sqrt{x}-2)}+\frac{3\sqrt{x}}{\sqrt{x}(\sqrt{x}-2)}\right]:\frac{(\sqrt{x}+2)(\sqrt{x}-2)-\sqrt{x}.\sqrt{x}}{\sqrt{x}(\sqrt{x}-2)}\)

\(=\frac{4\sqrt{x}-4}{\sqrt{x}(\sqrt{x}-2)}:\frac{x-4-x}{\sqrt{x}(\sqrt{x}-2)}=\frac{4(\sqrt{x}-1)}{\sqrt{x}(\sqrt{x}-2)}.\frac{\sqrt{x}(\sqrt{x}-2)}{-4}=1-\sqrt{x}\)