$B= \frac{3.\sqrt[]{x}+1}{x+2\sqrt[]{x}-3}-\frac{2}{\sqrt[]{x}+3}$
= $\frac{3.\sqrt[]{x}+1}{(\sqrt[]{x}-1).(\sqrt[]{x}+3)}-\frac{2.(\sqrt[]{x}-1)}{(\sqrt[]{x}).(\sqrt[]{x}+3})$
= $\frac{3.\sqrt[]{x}+1-2.(\sqrt[]{x}+2)}{(\sqrt[]{x}-1).(\sqrt[]{x}+3)}$
= $\frac{3.\sqrt[]{x}-2.(\sqrt[]{x}+3)}{(\sqrt[]{x}-1).(\sqrt[]{x}+3)}$
= $\frac{\sqrt[]{x}+3}{(\sqrt[]{x}-1).(\sqrt[]{x}+3)}$
= $\frac{1}{\sqrt[]{x}-1}$