so sánh A=10^11-1/10612-1 B=10^10+1/10^11+1

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1. Ta có:

   $A = \dfrac{10^{11}-1}{10^{12}-1}$

   $⇒ 10A = \dfrac{10^{12} – 10}{10^{12}-1}$

   $⇔ 10A = \dfrac{10^{12} – 1 – 9}{10^{12}-1}$

   $⇔ 10A = 1 – \dfrac{9}{10^{12}-1}$

   $B = \dfrac{10^{10}+1}{10^{11}+1}$

   $⇒ 10B = \dfrac{10^{11} + 10}{10^{11}+1}$

   $⇔ 10B = \dfrac{10^{11} + 1 + 9}{10^{11}+1}$

   $⇔ 10B = 1+ \dfrac{9}{10^{11}+1}$

    Mà $1 – \dfrac{9}{10^{12}-1} <1+ \dfrac{9}{10^{11}+1}$

   $⇒ 10A < 10B$

   $⇒ A < B$.

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