\(A=\left(\dfrac{x\sqrt{x}+1-\left(x-1\right)\left(\sqrt{x}-1\right)}{x-1}\right)\cdot\dfrac{\left(x-1\right)\left(x-4\right)}{x\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x\sqrt{x}+1-x\sqrt{x}+x+\sqrt{x}-1}{x-1}\cdot\dfrac{\left(x-4\right)\left(x-1\right)}{x\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x+\sqrt{x}}{1}\cdot\dfrac{x-4}{x\left(\sqrt{x}+1\right)}=\dfrac{x-4}{\sqrt{x}}\)