a.
ĐKXĐ : x $\geq$ 0, x $\neq$ 9
P = $\frac{2\sqrt{x}}{x-9}$ - $\frac{2}{\sqrt{x}+3}$
P = $\frac{2\sqrt{x}}{(\sqrt{x}-3)(\sqrt{x}+3)}$ - $\frac{2(\sqrt{x}-3)}{(\sqrt{x}+3)(\sqrt{x}-3)}$
P = $\frac{2\sqrt{x}-2\sqrt{x} +6}{(\sqrt{x}-3)(\sqrt{x}+3)}$
P = $\frac{6}{(\sqrt{x}-3)(\sqrt{x}+3)}$
b.
Q = $\frac{6}{3-\sqrt{x}}$
A = $\frac{Q}{P}$ = $\frac{6}{3-\sqrt{x}}$ . $\frac{(\sqrt{x}-3)(\sqrt{x}+3)}{6}$
A = - $\frac{(\sqrt{x}-3)(\sqrt{x}+3)}{\sqrt{x}-3}$
A = - $\sqrt{x}$ - 3
Thay A = $\frac{2\sqrt{x}+1}{2}$ ta có:
$\frac{2\sqrt{x}+1}{2}$v = - $\sqrt{x}$ - 3
⇔ 2$\sqrt{x}$ + 1 = - 2$\sqrt{x}$ - 6
⇔ 4$\sqrt{x}$ = -7
⇔ $\sqrt{x}$ = $\frac{-7}{4}$ (ktm)
⇒ x ∈ ∅
