ta có:\(\frac{x-2\sqrt{x}+1}{x-\sqrt{x}+1}=\frac{1}{2}\)
\(\Rightarrow x-3\sqrt{x}+1=0\)
\(\Rightarrow\hept{\begin{cases}x+1=3\sqrt{x}\\x-3\sqrt{x}=-1\end{cases}}\)
lại có \(B=\frac{3x\sqrt{x}+10x+19}{x^2+7x+15}\)
\(=\frac{3x\sqrt{x}-9x+19x+19}{x^2-9x+16x+15}\)
\(=\frac{3\sqrt{x}\left(x-3\sqrt{x}\right)+19\left(x+1\right)}{\left(x+3\sqrt{x}\right)\left(x-3\sqrt{x}\right)+16x+15}\)
\(=\frac{-3\sqrt{x}+19\times3\sqrt{x}}{-1\times\left(x+3\sqrt{x}\right)+16x+15}\)
\(=\frac{57\sqrt{x}-3\sqrt{x}}{15x+15-3\sqrt{x}}\)
\(=\frac{54\sqrt{x}}{15\left(x+1\right)-3\sqrt{x}}\)
\(=\frac{54\sqrt{x}}{45\sqrt{x}-3\sqrt{x}}\)
\(=\frac{54\sqrt{x}}{42\sqrt{x}}=\frac{27}{21}\)
