Toán Lớp 9: A=((√x – 1)/(√x + 1) – (√x + 1)/(√x – 1)):(1/2√x – √x/2). Rút gọn A
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Toán Lớp 9: A=((√x – 1)/(√x + 1) – (√x + 1)/(√x – 1)):(1/2√x – √x/2). Rút gọn A
Comments ( 2 )
DK:x > 0;x \ne 1\\
A = \left( {\dfrac{{\sqrt x – 1}}{{\sqrt x + 1}} – \dfrac{{\sqrt x + 1}}{{\sqrt x – 1}}} \right):\left( {\dfrac{1}{{2\sqrt x }} – \dfrac{{\sqrt x }}{2}} \right)\\
= \dfrac{{{{\left( {\sqrt x – 1} \right)}^2} – {{\left( {\sqrt x + 1} \right)}^2}}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}:\dfrac{{1 – x}}{{2\sqrt x }}\\
= \dfrac{{x – 2\sqrt x + 1 – x – 2\sqrt x – 1}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{2\sqrt x }}{{1 – x}}\\
= \dfrac{{ – 4\sqrt x }}{{\left( {x – 1} \right)}}.\dfrac{{2\sqrt x }}{{1 – x}}\\
= \dfrac{{8x}}{{{{\left( {x – 1} \right)}^2}}}
\end{array}\)