Question

cho biểu thức:

\(A=\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)

a) tìm ĐKXĐ và rút gọn A

b) tìm x để A = \(\frac{1}{2}\)

Answer 1

\(A=\frac{15\sqrt{x}-11-\left(3\sqrt{x}-2\right)\left(\sqrt{x}+3\right)-\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(A=\frac{15\sqrt{x}-11-3x-7\sqrt{x}+6-2x-\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(A=\frac{-5x+7\sqrt{x}-2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-\frac{2}{5}\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(A=\frac{\sqrt{x}-\frac{2}{5}}{\sqrt{x}+3}\)

Answer 2

Để \(A=\frac{1}{2}\Leftrightarrow\frac{\sqrt{x}-\frac{2}{5}}{\sqrt{x}+3}=\frac{1}{2}\Leftrightarrow\sqrt{x}=\frac{19}{5}\Leftrightarrow x=\frac{361}{25}\)