\(Q=\left(\text{}\text{}\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}+7}{x-2\sqrt{x}-3}\right):\frac{4-x}{\sqrt{x}+1}\)
\(=\left(\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}+7}{\left(x-2\sqrt{x}+1\right)-4}\right).\frac{\sqrt{x}+1}{4-x}\)
\(=\left(\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}+7}{\left(\sqrt{x}-1\right)^2-2^2}\right).\frac{\sqrt{x}+1}{4-x}\)
\(=\left(\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}+7}{\left(\sqrt{x}-1-2\right)\left(\sqrt{x}-1+2\right)}\right).\frac{\sqrt{x}+1}{4-x}\)
\(=\left(\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}+7}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\right).\frac{\sqrt{x}+1}{4-x}\)
\(=\left(\frac{\sqrt{x}-3+\sqrt{x}+7}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}\right).\frac{\sqrt{x}+1}{4-x}\)
\(=\frac{2\sqrt{x}+4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}.\frac{\sqrt{x}+1}{4-x}=\frac{\left(2\sqrt{x}+4\right).\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right).\left(2-\sqrt{x}\right)\left(\sqrt{x}+2\right)}\)
\(\frac{2\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-3\right)\left(2-\sqrt{x}\right)\left(\sqrt{x}+2\right)}=\frac{2}{\left(\sqrt{x}-3\right)\left(2-\sqrt{x}\right)}\)
