( can a/ 2 tru 1/ 2 can a ) nhan voi a tru can a / can a +1 tru a + can a / can a -1. Rut gon, giai chi tiet co dieu kien xac dinh

( can a/ 2 tru 1/ 2 can a ) nhan voi a tru can a / can a +1 tru a + can a / can a -1. Rut gon, giai chi tiet co dieu kien xac dinh

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  1. Đáp án:

    Giải thích các bước giải:

    \[\begin{array}{l}
    \left( {\frac{{\sqrt a }}{2} – \frac{1}{{2\sqrt a }}} \right)\left( {\frac{{a – \sqrt a }}{{\sqrt a + 1}} – \frac{{a + \sqrt a }}{{\sqrt a – 1}}} \right)\,\,\,\,\,\left( {DK:a > 0;a \ne 1} \right)\\
    = \frac{{a – 1}}{{2\sqrt a }} \cdot \left( {\frac{{\sqrt a {{\left( {\sqrt a – 1} \right)}^2} – \sqrt a {{\left( {\sqrt a + 1} \right)}^2}}}{{\left( {\sqrt a + 1} \right)\left( {\sqrt a – 1} \right)}}} \right)\\
    = \frac{{a – 1}}{{2\sqrt a }} \cdot \frac{{\sqrt a \cdot \left( {a – 2\sqrt a + 1 – a – 2\sqrt a – 1} \right)}}{{a – 1}}\\
    = \frac{{ – 4\sqrt a }}{2} = – 2\sqrt a
    \end{array}\]

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