Đáp án:
c. \(2 - 5\sqrt x = m\)
Giải thích các bước giải:
\(\begin{array}{l}
B = \dfrac{{15\sqrt x - 11 - \left( {2\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{15\sqrt x - 11 - 2x - \sqrt x + 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{ - 2x + 14\sqrt x - 8}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
P = A + B = \dfrac{{3\sqrt x - 2}}{{1 - \sqrt x }} + \dfrac{{ - 2x + 14\sqrt x - 8}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{ - \left( {3\sqrt x - 2} \right)\left( {\sqrt x + 3} \right) - 2x + 14\sqrt x - 8}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{ - 3x - 7\sqrt x + 6 - 2x + 14\sqrt x - 8}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{ - 5x + 7\sqrt x - 2}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{\left( {2 - 5\sqrt x } \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{2 - 5\sqrt x }}{{\sqrt x + 3}}\\
c.P\left( {\sqrt x + 3} \right) = m\\
\to \dfrac{{2 - 5\sqrt x }}{{\sqrt x + 3}}.\left( {\sqrt x + 3} \right) = m\\
\to 2 - 5\sqrt x = m
\end{array}\)
