\(P=\dfrac{10\sqrt{x}}{x+3\sqrt{x}-4}-\dfrac{2\sqrt{x}-3}{\sqrt{x}+4}+\dfrac{\sqrt{x}+1}{1-\sqrt{x}}\)
\(=\dfrac{10\sqrt{x}}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}-\dfrac{2\sqrt{x}-3}{\sqrt{x}+4}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\dfrac{10\sqrt{x}-\left(2\sqrt{x}-3\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}+4\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{10\sqrt{x}-\left(2x-5\sqrt{x}+3\right)-x-5\sqrt{x}-4}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-2x+5\sqrt{x}-3-x+5\sqrt{x}-4}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-3x+10\sqrt{x}-7}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}=\dfrac{-\left(\sqrt{x}-1\right)\left(3\sqrt{x}-7\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-\left(3\sqrt{x}-7\right)}{\sqrt{x}+4}\)
