## (2/căn3-1 +3/căn 3-2+15/3-căn 3)nhân 1/căn 3+5 rut gon

Question

(2/căn3-1 +3/căn 3-2+15/3-căn 3)nhân 1/căn 3+5 rut gon

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2 tháng 2021-07-24T20:16:21+00:00 1 Answers 2 views 0

## Answers ( )

1. Đáp án:

$$\dfrac{1}{2}$$

Giải thích các bước giải:

$$\begin{array}{l} \left( {\dfrac{2}{{\sqrt 3 – 1}} + \dfrac{3}{{\sqrt 3 – 2}} + \dfrac{{15}}{{3 – \sqrt 3 }}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ = \left( {\dfrac{{2\sqrt 3 + 2}}{{3 – 1}} + \dfrac{{3\sqrt 3 + 6}}{{3 – 4}} + \dfrac{{45 + 15\sqrt 3 }}{{9 – 3}}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ = \left( {\dfrac{{2\sqrt 3 + 2}}{2} – \dfrac{{3\sqrt 3 + 6}}{1} + \dfrac{{45 + 15\sqrt 3 }}{6}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ = \left( {\sqrt 3 + 1 – 3\sqrt 3 – 6 + \dfrac{{45 + 15\sqrt 3 }}{6}} \right).\dfrac{1}{{\sqrt 3 + 5}}\\ = \left[ {\dfrac{{6\left( { – 2\sqrt 3 – 5} \right) + 45 + 15\sqrt 3 }}{6}} \right].\dfrac{1}{{\sqrt 3 + 5}}\\ = \dfrac{{ – 12\sqrt 3 – 30 + 45 + 15\sqrt 3 }}{6}.\dfrac{1}{{\sqrt 3 + 5}}\\ = \dfrac{{3\sqrt 3 + 15}}{6}.\dfrac{1}{{\sqrt 3 + 5}}\\ = \dfrac{{3\left( {\sqrt 3 + 5} \right)}}{6}.\dfrac{1}{{\sqrt 3 + 5}}\\ = \dfrac{3}{6} = \dfrac{1}{2} \end{array}$$