0 bình luận về “(1/x-√x -1/√x-1) x-2√x+1/√x-1.rút gọn tìm đkxđ”
Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l} x \ge 0\\ x – \sqrt x \ne 0\\ \sqrt x – 1 \ne 0 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x \ge 0\\ x \ne 0\\ x \ne 1 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x > 0\\ x \ne 1 \end{array} \right.\)
Ta có:
\(\begin{array}{l} \left( {\dfrac{1}{{x – \sqrt x }} – \dfrac{1}{{\sqrt x – 1}}} \right).\dfrac{{x – 2\sqrt x + 1}}{{\sqrt x – 1}}\\ = \left( {\dfrac{1}{{\sqrt x .\left( {\sqrt x – 1} \right)}} – \dfrac{1}{{\sqrt x – 1}}} \right).\dfrac{{{{\left( {\sqrt x – 1} \right)}^2}}}{{\left( {\sqrt x – 1} \right)}}\\ = \dfrac{{1 – \sqrt x }}{{\sqrt x .\left( {\sqrt x – 1} \right)}}.\left( {\sqrt x – 1} \right)\\ = \dfrac{{1 – \sqrt x }}{{\sqrt x }} \end{array}\)
Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ge 0\\
x – \sqrt x \ne 0\\
\sqrt x – 1 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ge 0\\
x \ne 0\\
x \ne 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x > 0\\
x \ne 1
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
\left( {\dfrac{1}{{x – \sqrt x }} – \dfrac{1}{{\sqrt x – 1}}} \right).\dfrac{{x – 2\sqrt x + 1}}{{\sqrt x – 1}}\\
= \left( {\dfrac{1}{{\sqrt x .\left( {\sqrt x – 1} \right)}} – \dfrac{1}{{\sqrt x – 1}}} \right).\dfrac{{{{\left( {\sqrt x – 1} \right)}^2}}}{{\left( {\sqrt x – 1} \right)}}\\
= \dfrac{{1 – \sqrt x }}{{\sqrt x .\left( {\sqrt x – 1} \right)}}.\left( {\sqrt x – 1} \right)\\
= \dfrac{{1 – \sqrt x }}{{\sqrt x }}
\end{array}\)