Question

So sánh các phân số:

a) A=\(\frac{10^7+5}{10^7-8}\)   và    B=\(\frac{10^8+6}{10^8-7}\)

b)A=\(\frac{10^{1992}+1}{10^{1991}+1}\)  và  B=\(\frac{10^{1993}+1}{10^{1992}+1}\)

c)\(\frac{n}{n+3}\)  và  \(\frac{n-1}{n+4}\)

Answer 1

a) ta có A=\(\frac{10^7-8+13}{10^7-8}=1+\frac{13}{10^7-8}\)

             B=\(\frac{10^8-7+13}{10^8-7}=1+\frac{13}{10^8-7}\)

Vì 10^7-8 <10^8-7 nên 1+ 13/10^7-8>1+13/10^8-7

  Vậy A>B

Answer 2

câu a là A>B

Answer 3

Các bạn làm cả phần B và C có lời giải đi!!!

Answer 4

Ta có: \(A=\frac{10^{1992}+1}{10^{1991}+1}\)=> \(\frac{A}{10}=\frac{10^{1992}+1}{10.\left(10^{1991}+1\right)}\)=>\(\frac{A}{10}=\frac{10^{1992}+1}{10^{1992}+10}\)=>\(\frac{A}{10}=\frac{10^{1992}+10-9}{10^{1992}+10}\)=>\(\frac{A}{10}=\frac{10^{1992}+10}{10^{1992}+10}-\frac{9}{10^{1992}+10}\)=>\(\frac{A}{10}=1-\frac{9}{10^{1992}+10}\)

\(B=\frac{10^{1993}+1}{10^{1992}+1}\)=>\(\frac{B}{10}=\frac{10^{1993}+1}{10.\left(10^{1992}+1\right)}\)=>\(\frac{B}{10}=\frac{10^{1993}+1}{10^{1993}+10}\)=>\(\frac{B}{10}=\frac{10^{1993}+10-9}{10^{1993}+10}\)=>\(\frac{B}{10}=\frac{10^{1993}+10}{10^{1993}+10}-\frac{9}{10^{1993}+10}\)=>\(\frac{B}{10}=1-\frac{9}{10^{1993}+10}\)

Ta có: \(10^{1992}+10< 10^{1993}+10\)

=> \(\frac{1}{10^{1992}+10}>\frac{1}{10^{1993}+10}\)

=>\(1-\frac{1}{10^{1992}+10}< 1-\frac{1}{10^{1993}+10}\)

=> \(A< B\)

Answer 5

chim to vai lon