Đáp án:
\(P = \frac{{18 - 20\sqrt 5 }}{{ - \sqrt 5 \left( {4 - \sqrt 5 } \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ge 0;x \ne 9\\
P = \frac{{x\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)}} - \frac{{2\sqrt x - 6}}{{\sqrt x + 1}} - \frac{{\sqrt x + 3}}{{\sqrt x - 3}}\\
= \frac{{x\sqrt x - 3 - 2x + 6\sqrt x + 6\sqrt x - 18 - x - 6\sqrt x - 9}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)}}\\
= \frac{{x\sqrt x - 3x + 6\sqrt x - 30}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)}}\\
Thay:x = 14 - 6\sqrt 5 = 9 - 2.3.\sqrt 5 + 5 = {\left( {3 - \sqrt 5 } \right)^2}\\
\to P = \frac{{{{\left( {3 - \sqrt 5 } \right)}^2}\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} - 3.{{\left( {3 - \sqrt 5 } \right)}^2} + 6.\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} - 30}}{{\left( {\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} - 3} \right)\left( {\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} + 1} \right)}}\\
= \frac{{{{\left( {3 - \sqrt 5 } \right)}^3} - 3.{{\left( {3 - \sqrt 5 } \right)}^2} + 6\left( {3 - \sqrt 5 } \right) - 30}}{{\left( {3 - \sqrt 5 - 3} \right)\left( {3 - \sqrt 5 + 1} \right)}}\\
= \frac{{18 - 20\sqrt 5 }}{{ - \sqrt 5 \left( {4 - \sqrt 5 } \right)}}
\end{array}\)