Question

[Almira]

So sánh A và B

A=\(\frac{10^{11}-1}{10^{12}-1}\)           và         B=\(\frac{10^{10}+1}{10^{11}+1}\)

gợi ý:

nếu \(\frac{a}{b}\)>1 thì \(\frac{a}{b}\)>\(\frac{a+m}{b+m}\)         (m thuộc z)

        \(\frac{a}{b}\)<1 thì \(\frac{a}{b}\)<\(\frac{a+m}{b+m}\)

 A<1\(\) s\(\)uy ra A=\(\frac{10^{11}-1}{10^{12}-1}\)<\(\frac{10^{11}-1+11}{10^{12}-1+11}\)=\(\frac{10^{11}+10}{10^{12}+10}\)

Answer 1

[Almira]

ai biết thì giải hộ mình nha. Mình cảm ơn

Answer 2

[svtkvtm]

\(A=\frac{10^{11}-1}{10^{12}-1}\Leftrightarrow10A=1-\frac{9}{10^{12}-1};B=\frac{10^{10}+1}{10^{11}+1}\Rightarrow10B=1+\frac{9}{10^{11}+1}\Rightarrow10A< 10B\Rightarrow A< B\)