\(\begin{array}{l} 1)A = \dfrac{{2\sqrt x \left( {\sqrt x – 3} \right) + \left( {\sqrt x + 1} \right)\left( {\sqrt x + 3} \right) + 11\sqrt x – 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}\\ = \dfrac{{2x – 6\sqrt x + x + 4\sqrt x + 3 + 11\sqrt x – 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}\\ = \dfrac{{3x + 9\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}\\ = \dfrac{{3\sqrt x }}{{\sqrt x – 3}}\\ 2)B = \dfrac{{x + 12 + \sqrt x – 2 – 4\sqrt x – 8}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}\\ = \dfrac{{x – 3\sqrt x + 2}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}\\ = \dfrac{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}\\ = \dfrac{{\sqrt x – 1}}{{\sqrt x + 2}}\\ 3)C = \left[ {\dfrac{{x + \sqrt x + \sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}} \right]:\left[ {\dfrac{{2\sqrt x + 2 – 2 + x}}{{x\left( {\sqrt x + 1} \right)}}} \right]\\ = \dfrac{{x + 2\sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{x\left( {\sqrt x + 1} \right)}}{{x + 2\sqrt x }}\\ = \dfrac{x}{{\sqrt x – 1}}\\ 4)D = \left[ {\dfrac{{x + \sqrt x + 10 – \sqrt x – 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}} \right].\left( {\sqrt x – 3} \right)\\ = \dfrac{{x + 7}}{{\sqrt x + 3}}\\ 5)E = \dfrac{{x – 2 – \sqrt x – 2 + \sqrt x }}{{\sqrt x \left( {\sqrt x + 2} \right)}}\\ = \dfrac{{x – 4}}{{\sqrt x \left( {\sqrt x + 2} \right)}}\\ = \dfrac{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}{{\sqrt x \left( {\sqrt x + 2} \right)}}\\ = \dfrac{{\sqrt x – 2}}{{\sqrt x }}\\ 6)F = \left[ {\dfrac{{\sqrt x + 1 + \sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}} \right]:\left( {\dfrac{{\sqrt x – \sqrt x + 1}}{{\sqrt x – 1}}} \right)\\ = \dfrac{{2\sqrt x + 1}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x – 1}}{1}\\ = \dfrac{{2\sqrt x + 1}}{{\sqrt x + 1}}\\ 7)G = \left[ {\dfrac{{x + 3\sqrt x + \sqrt x – 5}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 5} \right)}}} \right].\dfrac{{\sqrt x – 5}}{{\sqrt x + 2}}\\ = \dfrac{{x + 4\sqrt x – 5}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 5} \right)}}.\dfrac{{\sqrt x – 5}}{{\sqrt x + 2}}\\ = \dfrac{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 1} \right)}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 5} \right)}}.\dfrac{{\sqrt x – 5}}{{\sqrt x + 2}}\\ = \dfrac{{\sqrt x – 1}}{{\sqrt x + 2}}\\ 8)H = \left[ {\dfrac{{\sqrt x + 1 + x}}{{\sqrt x \left( {\sqrt x + 1} \right)}}} \right]:\dfrac{{\sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}}\\ = \dfrac{{\sqrt x + 1 + x}}{{\sqrt x \left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x }}\\ = \dfrac{{x + \sqrt x + 1}}{{\sqrt x }} \end{array}\)
Answers ( )
Đáp án:
4) \(\dfrac{{x + 7}}{{\sqrt x + 3}}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)A = \dfrac{{2\sqrt x \left( {\sqrt x – 3} \right) + \left( {\sqrt x + 1} \right)\left( {\sqrt x + 3} \right) + 11\sqrt x – 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{2x – 6\sqrt x + x + 4\sqrt x + 3 + 11\sqrt x – 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{3x + 9\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{3\sqrt x }}{{\sqrt x – 3}}\\
2)B = \dfrac{{x + 12 + \sqrt x – 2 – 4\sqrt x – 8}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}\\
= \dfrac{{x – 3\sqrt x + 2}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}\\
= \dfrac{{\left( {\sqrt x – 1} \right)\left( {\sqrt x – 2} \right)}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}\\
= \dfrac{{\sqrt x – 1}}{{\sqrt x + 2}}\\
3)C = \left[ {\dfrac{{x + \sqrt x + \sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}} \right]:\left[ {\dfrac{{2\sqrt x + 2 – 2 + x}}{{x\left( {\sqrt x + 1} \right)}}} \right]\\
= \dfrac{{x + 2\sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{x\left( {\sqrt x + 1} \right)}}{{x + 2\sqrt x }}\\
= \dfrac{x}{{\sqrt x – 1}}\\
4)D = \left[ {\dfrac{{x + \sqrt x + 10 – \sqrt x – 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right)}}} \right].\left( {\sqrt x – 3} \right)\\
= \dfrac{{x + 7}}{{\sqrt x + 3}}\\
5)E = \dfrac{{x – 2 – \sqrt x – 2 + \sqrt x }}{{\sqrt x \left( {\sqrt x + 2} \right)}}\\
= \dfrac{{x – 4}}{{\sqrt x \left( {\sqrt x + 2} \right)}}\\
= \dfrac{{\left( {\sqrt x + 2} \right)\left( {\sqrt x – 2} \right)}}{{\sqrt x \left( {\sqrt x + 2} \right)}}\\
= \dfrac{{\sqrt x – 2}}{{\sqrt x }}\\
6)F = \left[ {\dfrac{{\sqrt x + 1 + \sqrt x }}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}} \right]:\left( {\dfrac{{\sqrt x – \sqrt x + 1}}{{\sqrt x – 1}}} \right)\\
= \dfrac{{2\sqrt x + 1}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x – 1}}{1}\\
= \dfrac{{2\sqrt x + 1}}{{\sqrt x + 1}}\\
7)G = \left[ {\dfrac{{x + 3\sqrt x + \sqrt x – 5}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 5} \right)}}} \right].\dfrac{{\sqrt x – 5}}{{\sqrt x + 2}}\\
= \dfrac{{x + 4\sqrt x – 5}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 5} \right)}}.\dfrac{{\sqrt x – 5}}{{\sqrt x + 2}}\\
= \dfrac{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 1} \right)}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x – 5} \right)}}.\dfrac{{\sqrt x – 5}}{{\sqrt x + 2}}\\
= \dfrac{{\sqrt x – 1}}{{\sqrt x + 2}}\\
8)H = \left[ {\dfrac{{\sqrt x + 1 + x}}{{\sqrt x \left( {\sqrt x + 1} \right)}}} \right]:\dfrac{{\sqrt x }}{{\sqrt x \left( {\sqrt x + 1} \right)}}\\
= \dfrac{{\sqrt x + 1 + x}}{{\sqrt x \left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x \left( {\sqrt x + 1} \right)}}{{\sqrt x }}\\
= \dfrac{{x + \sqrt x + 1}}{{\sqrt x }}
\end{array}\)
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