A = $\frac{x}{\sqrt[]{x}+1}$ - $\frac{\sqrt[]{x}}{x+\sqrt[]{x}}$
= $\frac{x}{\sqrt[]{x}+1}$ - $\frac{\sqrt[]{x}}{\sqrt[]{x}(\sqrt[]{x}+1)}$
= $\frac{x}{\sqrt[]{x}+1}$ - $\frac{1}{\sqrt[]{x}+1}$
= $\frac{x-1}{\sqrt[]{x}+1}$
= $\frac{(\sqrt[]{x}+1)(\sqrt[]{x}-1)}{\sqrt[]{x}+1}$
= $\sqrt[]{x}$-1