Question

Giúp em với

Answer 1

Lời giải:
a.

\(A=\left[\frac{(\sqrt{x}-1)(3\sqrt{x}+1)-(3\sqrt{x}-1)}{(3\sqrt{x}-1)(3\sqrt{x}+1)}+\frac{8\sqrt{x}}{(3\sqrt{x}-1)(3\sqrt{x}+1)}\right]:\frac{3\sqrt{x}+1-(3\sqrt{x}-2)}{3\sqrt{x}+1}\)

\(=\frac{3\sqrt{x}-5\sqrt{x}+8\sqrt{x}}{(3\sqrt{x}-1)(3\sqrt{x}+1)}:\frac{3}{3\sqrt{x}+1}=\frac{3\sqrt{x}(\sqrt{x}+1)}{(3\sqrt{x}+1)(3\sqrt{x}-1)}.\frac{3\sqrt{x}+1}{3}=\frac{\sqrt{x}(\sqrt{x}+1)}{3\sqrt{x}-1}\)

b. 

$A=\frac{6}{5}\Leftrightarrow \frac{\sqrt{x}(\sqrt{x}+1)}{3\sqrt{x}-1}=\frac{6}{5}$

$\Leftrightarrow 5(x+\sqrt{x})=6(3\sqrt{x}-1)$

$\Leftrightarrow 5x-13\sqrt{x}+6=0$

$\Leftrightarrow (\sqrt{x}-2)(5\sqrt{x}-3)=0$

$\Leftrightarrow x=4$ hoặc $x=\frac{9}{25}$