Toán Lớp 8: cho biểu thức A=(2+x/2-x-4x^2/x^2-4-2-x/2+x):1-2x/2-x rút gọn
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Toán Lớp 8: cho biểu thức A=(2+x/2-x-4x^2/x^2-4-2-x/2+x):1-2x/2-x rút gọn
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DK:x \ne \left\{ { – 2;\dfrac{1}{2};2} \right\}\\
A = \left( {\dfrac{{2 + x}}{{2 – x}} – \dfrac{{4{x^2}}}{{{x^2} – 4}} – \dfrac{{2 – x}}{{x + 2}}} \right):\dfrac{{1 – 2x}}{{2 – x}}\\
= \dfrac{{{{\left( {x + 2} \right)}^2} + 4{x^2} – {{\left( {2 – x} \right)}^2}}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{2 – x}}{{1 – 2x}}\\
= \dfrac{{{x^2} + 4x + 4 + 4{x^2} – 4 + 4x – {x^2}}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{2 – x}}{{1 – 2x}}\\
= \dfrac{{4{x^2} + 8x}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{2 – x}}{{1 – 2x}}\\
= \dfrac{{4x\left( {x + 2} \right)}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{2 – x}}{{1 – 2x}}\\
= \dfrac{{4x}}{{1 – 2x}}
\end{array}\)