Question

Rút gọn biểu thức sau:

\(C=\left(\frac{x}{x+3\sqrt{x}}+\frac{1}{\sqrt{x}+3}\right):\left(1-\frac{2}{\sqrt{x}}+\frac{6}{x+3\sqrt{x}}\right)\)

Answer 1

ĐKXĐ: \(x>0\)

\(C=\left(\frac{\left(\sqrt{x}\right)^2}{\sqrt{x}\left(\sqrt{x}+3\right)}+\frac{1}{\sqrt{x}+3}\right):\left(\frac{x+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}-\frac{2\left(\sqrt{x}+3\right)}{\sqrt{x}\left(\sqrt{x}+3\right)}+\frac{6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\\ =\left(\frac{\sqrt{x}+1}{\sqrt{x}+3}\right):\left(\frac{x+3\sqrt{x}-2\sqrt{x}-3+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\\ =\left(\frac{\sqrt{x}+1}{\sqrt{x}+3}\right):\left(\frac{x+\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\\ =\frac{\sqrt{x}-1}{\sqrt{x}-3}\cdot\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{x+\sqrt{x}+3}\\ =\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{x+\sqrt{x}+3}\)

P/s: Bạn xem lại đề, chứ để thế này phân số xấu quá '-'