Rút gọn biểu thức a, (3y – 5x)^2 – (5x+3y)*(10x – 6y) + (5x + 3y)^2 b, (2/x+1 – 1/x-1) * x^2 – 1/x^2 – 6x + 9 – x-1/2x – 6

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1. Đáp án:

   a) \(36{y^2}\)

   Giải thích các bước giải:

   \(\begin{array}{l}
   a){(3y – 5x)^2} – (5x + 3y)(10x – 6y) + {(5x + 3y)^2}\\
    = {(5x – 3y)^2} – 2(5x + 3y)(5x – 3y) + {(5x + 3y)^2}\\
    = {\left( {5x – 3y – 5x – 3y} \right)^2} = 36{y^2}\\
   b)\left( {\dfrac{2}{{x + 1}} – \dfrac{1}{{x – 1}}} \right).\dfrac{{{x^2} – 1}}{{{x^2} – 6x + 9}} – \dfrac{{x – 1}}{{2x – 6}}\\
    = \dfrac{{2x – 2 – x – 1}}{{{x^2} – 1}}.\dfrac{{{x^2} – 1}}{{{x^2} – 6x + 9}} – \dfrac{{x – 1}}{{2x – 6}}\\
    = \dfrac{{x – 3}}{{{{\left( {x – 3} \right)}^2}}} – \dfrac{{x – 1}}{{2\left( {x – 3} \right)}}\\
    = \dfrac{1}{{x – 3}} – \dfrac{{x – 1}}{{2\left( {x – 3} \right)}}\\
    = \dfrac{{2 – x + 1}}{{2\left( {x – 3} \right)}} = \dfrac{{3 – x}}{{2\left( {x – 3} \right)}} =  – \dfrac{1}{2}
   \end{array}\)

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