0 bình luận về “rút gọn biểu thức:
A= $\frac{√(x ³)}{√xy – 2y}$ – $\frac{2x}{x+√x -2 √xy -2 √y}$ x $\frac{1-x}{1-√x
}$”
Đáp án:
$\begin{array}{l} A = \dfrac{{\sqrt {{x^3}} }}{{\sqrt {xy} – 2y}}\\ – \dfrac{{2x}}{{x + \sqrt x – 2\sqrt {xy} – 2\sqrt y }}.\dfrac{{1 – x}}{{1 – \sqrt x }}\\ = \dfrac{{x\sqrt x }}{{\sqrt y \left( {\sqrt x – 2\sqrt y } \right)}}\\ – \dfrac{{2x}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x – 2\sqrt y } \right)}}.\dfrac{{\left( {1 – \sqrt x } \right)\left( {1 + \sqrt x } \right)}}{{1 – \sqrt x }}\\ = \dfrac{{x\sqrt x }}{{\sqrt y .\left( {\sqrt x – 2\sqrt y } \right)}} – \dfrac{{2x}}{{x – 2\sqrt y }}\\ = \dfrac{{x\sqrt x – 2x\sqrt y }}{{\sqrt y \left( {x – 2\sqrt y } \right)}}\\ = \dfrac{{x\left( {\sqrt x – 2\sqrt y } \right)}}{{\sqrt y \left( {x – 2\sqrt y } \right)}}\\ = \dfrac{x}{{\sqrt y }} \end{array}$
Đáp án:
$\begin{array}{l}
A = \dfrac{{\sqrt {{x^3}} }}{{\sqrt {xy} – 2y}}\\
– \dfrac{{2x}}{{x + \sqrt x – 2\sqrt {xy} – 2\sqrt y }}.\dfrac{{1 – x}}{{1 – \sqrt x }}\\
= \dfrac{{x\sqrt x }}{{\sqrt y \left( {\sqrt x – 2\sqrt y } \right)}}\\
– \dfrac{{2x}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x – 2\sqrt y } \right)}}.\dfrac{{\left( {1 – \sqrt x } \right)\left( {1 + \sqrt x } \right)}}{{1 – \sqrt x }}\\
= \dfrac{{x\sqrt x }}{{\sqrt y .\left( {\sqrt x – 2\sqrt y } \right)}} – \dfrac{{2x}}{{x – 2\sqrt y }}\\
= \dfrac{{x\sqrt x – 2x\sqrt y }}{{\sqrt y \left( {x – 2\sqrt y } \right)}}\\
= \dfrac{{x\left( {\sqrt x – 2\sqrt y } \right)}}{{\sqrt y \left( {x – 2\sqrt y } \right)}}\\
= \dfrac{x}{{\sqrt y }}
\end{array}$