`P=\frac{a\sqrt{a}+a-1}{\sqrt{a}-1}-\frac{\sqrt{a}+1}{a-1} \ ( a\ne 1, a\ge 0)`
`P=\frac{a\sqrt{a}+a-1}{\sqrt{a}-1}-\frac{\sqrt{a}+1}{(\sqrt{a}+1)(\sqrt{a}-1)}`
`P=\frac{(\sqrt{a}+1)(a\sqrt{a}+a-1)-\sqrt{a}-1}{(\sqrt{a}+1)(\sqrt{a}-1)}`
`P=\frac{a^2+a-\sqrt{a}+2a\sqrt{a}-1-\sqrt{a}-1}{a-1}`
`P=\frac{a^2+a+2a\sqrt{a}-2\sqrt{a}-2}{a-1}`
`P=\frac{a^2-a+2a-2+2\sqrt{a}(a-1)}{a-1}`
`P=\frac{a(a-1)+2(a-1)+2\sqrt{a}(a-1)}{a-1}`
`P=\frac{(a-1)(a+2+2\sqrt{a})}{a-1}`
`P=a+2+2\sqrt{a}`
