Toán Lớp 9: 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
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Toán Lớp 9: 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
Comments ( 1 )
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}$