A= (1/x+2√x - 1/√x+2) : 1- √x/ x+4√x +4 a) Rút gọn bt A b) Tìm x để A=5/3 giúp mk gấp nha! sẽ vote và ctlhn
1 câu trả lời
Đáp án:
$\begin{array}{l}
a)Dkxd:x > 0;x \ne 1\\
A = \left( {\dfrac{1}{{x + 2\sqrt x }} - \dfrac{1}{{\sqrt x + 2}}} \right):\dfrac{{1 - \sqrt x }}{{x + 4\sqrt x + 4}}\\
= \left( {\dfrac{1}{{\sqrt x \left( {\sqrt x + 2} \right)}} - \dfrac{1}{{\sqrt x + 2}}} \right).\dfrac{{{{\left( {\sqrt x + 2} \right)}^2}}}{{1 - \sqrt x }}\\
= \dfrac{{1 - \sqrt x }}{{\sqrt x \left( {\sqrt x + 2} \right)}}.\dfrac{{{{\left( {\sqrt x + 2} \right)}^2}}}{{1 - \sqrt x }}\\
= \dfrac{{\sqrt x + 2}}{{\sqrt x }}\\
b)A = \dfrac{5}{3}\\
\Leftrightarrow \dfrac{{\sqrt x + 2}}{{\sqrt x }} = \dfrac{5}{3}\\
\Leftrightarrow 3\sqrt x + 6 = 5\sqrt x \\
\Leftrightarrow 2\sqrt x = 6\\
\Leftrightarrow \sqrt x = 3\\
\Leftrightarrow x = 9\left( {tmdk} \right)\\
Vậy\,x = 9
\end{array}$