\(P=\left(1+\dfrac{\sqrt{a}}{a+1}\right):\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a\sqrt{a}+\sqrt{a}-a-1}\right)\\ P=\dfrac{a+\sqrt{a}+1}{a+1}:\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a\left(\sqrt{a}-1\right)+\left(\sqrt{a}-1\right)}\right)\\ P=\dfrac{a+\sqrt{a}+1}{a+1}:\dfrac{a+1+2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(a+1\right)}\\ P=\dfrac{a+\sqrt{a}+1}{a+1}:\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(a+1\right)}\\ P=\dfrac{a+\sqrt{a}+1}{a+1}\cdot\dfrac{\left(\sqrt{a}-1\right)\left(a+1\right)}{\left(\sqrt{a}+1\right)^2}\\ P=\dfrac{\sqrt{a^3}-1}{\left(\sqrt{a}+1\right)^2}\)
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