Rút gọn B=(2+x/2-x+4x^2/x^2-4-2-x/2+x)/x^2-3x/2x^2-x^3

0 bình luận về “Rút gọn B=(2+x/2-x+4x^2/x^2-4-2-x/2+x)/x^2-3x/2x^2-x^3”

1. Đáp án:

   \(\dfrac{{4{x^2}\left( {2 – x} \right)}}{{\left( {x + 2} \right)\left( {x – 3} \right)}}\)

   Giải thích các bước giải:

   \(\begin{array}{l}
   B = \left( {\dfrac{{2 + x}}{{2 – x}} + \dfrac{{4{x^2}}}{{{x^2} – 4}} – \dfrac{{2 – x}}{{2 + x}}} \right):\dfrac{{{x^2} – 3x}}{{2{x^2} – {x^3}}}\\
    = \left[ {\dfrac{{{{\left( {x + 2} \right)}^2} – 4{x^2} – {{\left( {2 – x} \right)}^2}}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}} \right].\dfrac{{{x^2}\left( {2 – x} \right)}}{{x\left( {x – 3} \right)}}\\
    = \dfrac{{{x^2} + 4x + 4 – 4{x^2} – 4 + 4x – {x^2}}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{{x^2}\left( {2 – x} \right)}}{{x\left( {x – 3} \right)}}\\
    = \dfrac{{ – 4{x^2} + 8x}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{{x^2}\left( {2 – x} \right)}}{{x\left( {x – 3} \right)}}\\
    = \dfrac{{ – 4x\left( {x – 2} \right)}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{{x^2}\left( {2 – x} \right)}}{{x\left( {x – 3} \right)}}\\
    = \dfrac{{4x\left( {2 – x} \right)}}{{\left( {2 – x} \right)\left( {x + 2} \right)}}.\dfrac{{{x^2}\left( {2 – x} \right)}}{{x\left( {x – 3} \right)}}\\
    = \dfrac{{4{x^2}\left( {2 – x} \right)}}{{\left( {x + 2} \right)\left( {x – 3} \right)}}
   \end{array}\)

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