rút gọn $\frac{\frac{12(1+\sqrt{x})^{11}.x^{6}}{2\sqrt{x}}-\frac{2\sqrt{x}(1+\sqrt{x})^{12}.6x^{5}}{2\sqrt{x}}}{x^{12}}$

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1. Đáp án:

    $\dfrac{-6(1+\sqrt{x})^{11}}{x^{7}}\\ $ 

   Giải thích các bước giải:

   $\dfrac{\dfrac{12(1+\sqrt{x})^{11}x^6}{2\sqrt{x}}-\dfrac{2\sqrt{x}(1+\sqrt{x})^{12}.6x^5}{2\sqrt{x}}}{x^{12}}\\
   =\dfrac{12(1+\sqrt{x})^{11}x^6-2\sqrt{x}(1+\sqrt{x})^{12}.6x^5}{x^{12}.2\sqrt{x}}\\ \\

   =\dfrac{2x^5\left [6(1+\sqrt{x})^{11}x-\sqrt{x}(1+\sqrt{x})^{12}.6  \right ]}{x^{12}.2\sqrt{x}}\\ \\
   =\dfrac{\left [6(1+\sqrt{x})^{11}x-\sqrt{x}(1+\sqrt{x})^{12}.6  \right ]}{x^{7}.\sqrt{x}}\\ \\
   =\dfrac{6\sqrt{x}(1+\sqrt{x})^{11}\left [\sqrt{x}-(1+\sqrt{x})  \right ]}{x^{7}.\sqrt{x}}\\ \\
   =\dfrac{6(1+\sqrt{x})^{11}\left [\sqrt{x}-1-\sqrt{x}  \right ]}{x^{7}}\\ \\
   =\dfrac{-6(1+\sqrt{x})^{11}}{x^{7}}\\ $ 

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