Question

Rút gọn biểu thức A = \(\left(1+\frac{5}{\sqrt{x}-2}\right).\left(\sqrt{x}-\frac{x+2\sqrt{x}+4}{\sqrt{x}+3}\right)\)

Answer 1

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

Ta có:

\(A=\left(\frac{\sqrt{x}-2+5}{\sqrt{x}-2}\right)\cdot\left(\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{\sqrt{x}+3}-\frac{x+2\sqrt{x}+4}{\sqrt{x}+3}\right)\\ =\frac{\sqrt{x}+3}{\sqrt{x}-2}\cdot\left(\frac{x+3\sqrt{x}-x-2\sqrt{x}-4}{\sqrt{x}+3}\right)\\ =\frac{\sqrt{x}+3}{\sqrt{x}-2}\cdot\frac{\sqrt{x}-4}{\sqrt{x}+3}\\ =\frac{\sqrt{x}-4}{\sqrt{x}-2}\left(=1-\frac{2}{\sqrt{x}-2}\right)\)