A=2/3.(2014/2013-1/2013)+1/3=2/3.1+1/3=3/3=1

Bài 1: Tính giá trị các biểu thức:

 1) \(A=\frac{2}{3}.\frac{2014}{2013}-\frac{2}{3}.\frac{1}{2013}+\frac{1}{3}\)

\(=\frac{2}{3}.\left(\frac{2014}{2013}-\frac{1}{2013}\right)+\frac{1}{3}\)

\(=\frac{2}{3}.1+\frac{1}{3}\)

= 1

5\(\frac{8}{17}\) : x - (\(\frac{8}{17}\)) : x + 3\(\frac{1}{17}\): 17\(\frac13\) = \(\frac{4}{17}\)

(5\(\frac{8}{17}\) - \(\frac{8}{17}\)) : x + \(\frac{52}{17}\) : \(\frac{52}{3}\) = \(\frac{4}{17}\)

5:x + \(\frac{52}{17}\times\) \(\frac{3}{52}\) = \(\frac{4}{17}\)

5 : x + \(\frac{3}{17}\) = \(\frac{4}{17}\)

5 : x = \(\frac{4}{17}\) - \(\frac{3}{17}\)

5 : x = \(\frac{1}{17}\)

x = 5 : \(\frac{1}{17}\)

x = 5 x 17

x = 85

Vậy x = 85

1/1.4 + 1/4.7 + ...+1/x(x+3) = 6/19

3/1.4 + 3/4.7 +..+3/x(x+3) = 18/19

1/1 - 1/4+ 1/4 - 1/7 +...+1/x-1/(x+3) = 1 - 1/19

1- 1/(x+3) = 1 - 1/19

1/(x+3) = 1/19

x + 3 = 19

x = 19 - 3

x = 16

Vậy x = 16

a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)

Ta có chính chất phân số trung gian là \(\frac{2^{10}+1}{2^{10}-3}\)

\(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}\) ; \(\frac{2^{10}-1}{2^{10}-3}< \frac{2^{10}+1}{2^{10}-3}\)

Vì \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}>\frac{2^{10}-1}{2^{10}-3}\)

Nên \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}-1}{2^{10}-3}\)

b) \(A=\frac{2011}{2012}+\frac{2012}{2013}\)và \(B=\frac{2011+2012}{2012+2013}\)

Ta có : \(A=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}=B\)

Vậy A > B 

Có gì  sai cho sorry

a,

\(\frac{2^{10}+1}{2^{10}-1}=1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}=\frac{2^{10}-1}{2^{10}-3}\)

b,

\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)