Đáp án:
\(P = \dfrac{\sqrt x- 4}{\sqrt x - 1}\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad P = \dfrac{3x+5\sqrt x - 4}{\left(\sqrt x + 3\right)\left(\sqrt x - 1\right)} - \dfrac{\sqrt x + 1}{\sqrt x + 3} - \dfrac{\sqrt x + 3}{\sqrt x - 1}\qquad (x\geq 0;\, x \ne 1)\\
\to P = \dfrac{3x+5\sqrt x - 4 -\left(\sqrt x + 1\right)\left(\sqrt x - 1\right) -\left(\sqrt x + 3\right)^2}{\left(\sqrt x + 3\right)\left(\sqrt x - 1\right)}\\
\to P = \dfrac{3x+5\sqrt x - 4 - (x-1) - \left(x + 6\sqrt x + 9\right)}{\left(\sqrt x + 3\right)\left(\sqrt x - 1\right)}\\
\to P = \dfrac{x - \sqrt x - 12}{\left(\sqrt x + 3\right)\left(\sqrt x - 1\right)}\\
\to P = \dfrac{\left(\sqrt x + 3\right)\left(\sqrt x - 4\right)}{\left(\sqrt x + 3\right)\left(\sqrt x - 1\right)}\\
\to P = \dfrac{\sqrt x- 4}{\sqrt x - 1}
\end{array}\)
