a) Ta có: \(A=\left(\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\cdot\dfrac{\left(1-x\right)^2}{2}\)
\(=\left(\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)^2\cdot\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)^2\cdot\left(\sqrt{x}-1\right)}\right)\cdot\dfrac{\left(x-1\right)^2}{2}\)
\(=\dfrac{x+\sqrt{x}-2\sqrt{x}-2-\left(x-\sqrt{x}+2\sqrt{x}-2\right)}{\left(\sqrt{x}+1\right)^2\cdot\left(\sqrt{x}-1\right)}\cdot\dfrac{\left(\sqrt{x}+1\right)^2\cdot\left(\sqrt{x}-1\right)^2}{2}\)
\(=\dfrac{x-\sqrt{x}-2-x-\sqrt{x}+2}{2}\cdot\dfrac{\sqrt{x}-1}{1}\)
\(=\dfrac{-2\sqrt{x}}{2}\cdot\left(\sqrt{x}-1\right)\)
\(=-\sqrt{x}\cdot\left(\sqrt{x}-1\right)\)
\(=-x+1\)
b) Để A=-6 thì -x+1=-6
\(\Leftrightarrow-x=-6-1=-7\)
hay x=7(thỏa ĐK)
Vậy: Để A=-6 thì x=7
