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