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