Question

45. CIOOA = ((sqrt(x) - 4)/(sqrt(x) * (sqrt(x) - 2)) + 3/(sqrt(x) - 2)) / ((sqrt(x) + 2)/(sqrt(x)) - (sqrt(x))/(sqrt(x) - 2)) a) Rút gọn A VỚI x > 0 , x ne4 b ) Tỉnh A với x = 6 - 2sqrt(5)

Answer 1

a: Ta có: \(A=\left(\frac{\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}+\frac{3}{\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}-2}\right)\)

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

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

b: Khi \(x=6-2\sqrt5=\left(\sqrt5-1\right)^2\) thì \(A=-\sqrt{\left(\sqrt5-1\right)^2}+1\)

\(=-\left(\sqrt5-1\right)+1=-\sqrt5+1+1=-\sqrt5+2\)