\(A=\dfrac{x\sqrt{x}+1-\left(x-1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x\sqrt{x}+1-x\sqrt{x}+x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x+\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
\(A=\dfrac{x\sqrt{x}+1}{x-1}-\dfrac{x-1}{\sqrt{x}+1}\) (ĐK: \(x\ge0;x\ne1\))
\(A=\dfrac{\left(\sqrt{x}\right)^3+1^3}{\left(\sqrt{x}\right)^2-1^2}-\dfrac{\left(\sqrt{x}\right)^2-1^2}{\sqrt{x}+1}\)
\(A=\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\sqrt{x}+1}\)
\(A=\dfrac{x-\sqrt{x}+1}{\sqrt{x}-1}-\left(\sqrt{x}-1\right)\)
\(A=\dfrac{x-\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}-1}\)
\(A=\dfrac{x-\sqrt{x}+1-\left(\sqrt{x}-1\right)^2}{\sqrt{x}-1}\)
\(A=\dfrac{x-\sqrt{x}+1-x+2\sqrt{x}-1}{\sqrt{x}-1}\)
\(A=\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
