\(A=\left(1+\frac{2-2\sqrt{x}}{x-1}\right):\left(\frac{1}{\sqrt{x}+1}-\frac{x}{x\sqrt{x}+1}\right)\)
\(=\left(1-\frac{2\left(1-\sqrt{x}\right)}{1-x}\right):\left(\frac{x\sqrt{x}+1-x\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(x\sqrt{x}+1\right)}\right)\)
\(=\left(1-\frac{2}{1+\sqrt{x}}\right):\left(\frac{x\sqrt{x}+1-x\sqrt{x}-x}{\left(\sqrt{x}+1\right)\left(x\sqrt{x}+1\right)}\right)\)
\(=\frac{1+\sqrt{x}-2}{1+\sqrt{x}}:\frac{1-x}{\left(\sqrt{x}+1\right)\left(x\sqrt{x}+1\right)}=\frac{\sqrt{x}-1}{1+\sqrt{x}}.\frac{\left(\sqrt{x}+1\right)\left(x\sqrt{x}+1\right)}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}\)
\(=\frac{-x\sqrt{x}+1}{1+\sqrt{x}}\)
Thay x = 25 vào biểu thức A ta được :
\(A=\frac{-25\sqrt{25}+1}{1+\sqrt{25}}=-21\)
Vậy khi x = 25 thì giá trị của biểu thức A là -21
