`A=(\frac{\sqrt[a]}{\sqrt[a]+\sqrt[b]}+\frac{a}{b-a}):(\frac{\sqrt[a]}{\sqrt[a]+\sqrt[b]}-\frac{a}{a+b+2\sqrt[ab]})`
`A=(\frac{\sqrt[a]}{\sqrt[a]+\sqrt[b]}+\frac{a}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}):(\frac{\sqrt[a]}{\sqrt[a]+\sqrt[b]}-\frac{a}{(\sqrt[a]+\sqrt[b])^2})`
`A=\frac{\sqrt[a](\sqrt[b]-\sqrt[a])+a}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}:\frac{\sqrt[a].(\sqrt[a]+\sqrt[b])-a}{(\sqrt[a]+\sqrt[b])^2}`
`A=\frac{\sqrt[ab]}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}:\frac{\sqrt[ab]}{(\sqrt[a]+\sqrt[b])^2}`
`A=\frac{\sqrt[ab]}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}.\frac{(\sqrt[a]+\sqrt[b])^2}{\sqrt[ab]}`
`A=\frac{\sqrt[a]+\sqrt[b]}{\sqrt[b]-\sqrt[a]}`
Theo đề bài: `A-\frac{a+b-2\sqrt[ab]}{b-a}`
`=\frac{\sqrt[a]+\sqrt[b]}{\sqrt[b]-\sqrt[a]}-\frac{(\sqrt[a]-\sqrt[b])^2}{b-a}`
`=\frac{\sqrt[a]+\sqrt[b]}{\sqrt[b]-\sqrt[a]}-\frac{(\sqrt[a]-\sqrt[b])^2}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}`
`=\frac{(\sqrt[a]+\sqrt[b])^2-(\sqrt[a]-\sqrt[b])^2}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}`
`=\frac{(\sqrt[a]+\sqrt[b]+\sqrt[a]-\sqrt[b])(\sqrt[a]+\sqrt[b]-\sqrt[a]+\sqrt[b])}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}`
`=\frac{2\sqrt[a].2\sqrt[b]}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}`
`=\frac{4\sqrt[ab]}{(\sqrt[b]-\sqrt[a])(\sqrt[b]+\sqrt[a])}`
