Giải thích các bước giải:
\(\begin{array}{l}
B8:\\
a.DK:x > 0;x \ne 1\\
B = \frac{{\sqrt x + 1}}{{\sqrt x }}:\left[ {\frac{{\sqrt x - 1 + \sqrt x + 1 - 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}} \right]\\
= \frac{{\sqrt x + 1}}{{\sqrt x }}:\left( {\frac{{2\sqrt x - 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}} \right)\\
= \frac{{\sqrt x + 1}}{{\sqrt x }}.\frac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{2\left( {\sqrt x - 1} \right)}}\\
= \frac{{x + 2\sqrt x + 1}}{{2\sqrt x }}\\
b.B = 3\\
\to \frac{{x + 2\sqrt x + 1}}{{2\sqrt x }} = 3\\
\to x + 2\sqrt x + 1 = 6\sqrt x \\
\to x - 4\sqrt x + 1 = 0\\
\to \left[ \begin{array}{l}
\sqrt x = 2 + \sqrt 3 \\
\sqrt x = 2 - \sqrt 3
\end{array} \right. \to \left[ \begin{array}{l}
x = 7 + 4\sqrt 3 \\
x = 7 - 4\sqrt 3
\end{array} \right.\\
B9:\\
a.DK:x \ge 0;x \ne 25\\
C = \frac{{x + 5\sqrt x - 10\sqrt x - 5\sqrt x + 25}}{{\left( {\sqrt x - 5} \right)\left( {\sqrt x + 5} \right)}}\\
= \frac{{{{\left( {\sqrt x - 5} \right)}^2}}}{{\left( {\sqrt x - 5} \right)\left( {\sqrt x + 5} \right)}} = \frac{{\sqrt x - 5}}{{\sqrt x + 5}}\\
b.x = 9 \to C = - \frac{1}{4}\\
c.C < \frac{1}{3}\\
\to \frac{{\sqrt x - 5}}{{\sqrt x + 5}} < \frac{1}{3}\\
\to \frac{{3\sqrt x - 15 - \sqrt x - 5}}{{3\sqrt x + 15}} < 0\\
\to \frac{{2\sqrt x - 20}}{{3\sqrt x + 15}} < 0\\
\to 2\sqrt x - 20 < 0\left( {do:3\sqrt x + 15 > 0\forall x \ge 0} \right)\\
\to \sqrt x < 10\\
\to 0 \le x < 100;x \ne 25
\end{array}\)
