( $\frac{\sqrt[]{a}+\sqrt[]{b}}{\sqrt[]{a}-\sqrt[]{b}}$- $\frac{\sqrt[]{a}-\sqrt[]{b}}{\sqrt[]{a}+\sqrt[]{b}}$).( a-b)
= $\frac{(\sqrt[]{a}+\sqrt[]{b})^{2}-(\sqrt[]{a}-\sqrt[]{b})^{2}}{(\sqrt[]{a}-\sqrt[]{b}).(\sqrt[]{a}+\sqrt[]{b})}$.( a-b)
= $\frac{4.\sqrt[]{ab}}{a-b}$.(a-b)
= $4.\sqrt[]{ab}$