Rút gọn biểu thức: P = căn bậc hai x / (căn bậc hai x + 3) + 2 căn bậc hai x / (căn bậc hai x
Rút gọn biểu thức: \(P = \frac{{\sqrt x }}{{\sqrt x + 3}} + \frac{{2\sqrt x }}{{\sqrt x - 3}} - \frac{{3x + 9}}{{x - 9}}\).
ĐKXĐ: x ≥ 0; x ≠ 9.
\(P = \frac{{\sqrt x }}{{\sqrt x + 3}} + \frac{{2\sqrt x }}{{\sqrt x - 3}} - \frac{{3x + 9}}{{x - 9}}\)
\( = \frac{{\sqrt x \left( {\sqrt x - 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}} + \frac{{2\sqrt x \left( {\sqrt x + 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}} - \frac{{3x + 9}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\)
\( = \frac{{x - 3\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}} + \frac{{2x + 6\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}} - \frac{{3x + 9}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\)
\( = \frac{{x - 3\sqrt x + 2x + 6\sqrt x - 3x - 9}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\)
\( = \frac{{3\sqrt x + 9}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\)
\( = \frac{{3\left( {\sqrt x + 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\)
\( = \frac{3}{{\sqrt x - 3}}\).