A=4052170

B=1/1/2012

Ta thấy \(\frac{2012.2013}{2012.2013+1}< 1\) ; \(\frac{2013}{2012}>1\)

\(\Rightarrow\frac{2012.2013}{2012.2013+1}< \frac{2013}{2012}\)

Ta thấy phân số \(\frac{2012\cdot2013}{2012\cdot2013+1}\)có tử số nhỏ hơn mẫu số  => Phân số này < 1 

Mà phân số \(\frac{2013}{2012}\)> 1 => Phân số \(\frac{2012\cdot2013}{2012\cdot2013+1}\)< \(\frac{2013}{2012}\)

Ta có : 

\(\frac{2012.2013}{2012.2013+1}< \frac{2012.2013+1}{2012.2013+1}=1\left(1\right)\)

\(\frac{2013}{2012}>\frac{2012}{2012}=1\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\)

\(\Rightarrow\frac{2012.2013}{2012.2013+1}< \frac{2013}{2012}\)

\(=1+\dfrac{1}{2012}-1-\dfrac{1}{2013}-\dfrac{1}{2012}+\dfrac{1}{2013}=0\)

= 0

\(\dfrac{1}{4050156}\) - \(\dfrac{1}{2012x2013}\)

=

\(A=\frac{2012\times2013-1}{2011\times2013+2012}\)

\(A=\frac{2012\times2013-1}{2011\times2013+2011+1}\)

\(A=\frac{2012\times2013-1}{2013\times\left(2011+1\right)+1}\)

\(A=\frac{2012\times2013-1}{2013\times2012+1}\)

\(A=\frac{2012\times2013+1-2}{2012\times2013+1}\)

\(A=1-\frac{2}{2012\times2013+1}\)

Tính tử số 2012x2013-1=2011x2013+2013-1=2011x2013+2012

Do tử=mẫu =2011x2013=2012

Suy ra: A=1

\(A=\frac{2012\times2013-1}{2011\times2013+2012}\)

\(A=\frac{\left(2011+1\right)\times2013-1}{2011\times2013+2012}=\frac{2011\times2013+2013-1}{2011\times2013+2012}=\frac{2011\times2013+2012}{2011\times2013+2012}=1\)

Trả lời

2012.2013-1/2011.2013+2012

=2011.2013+2012-1/2011.2013+2012

=-1/1

=-1.

Học tốt !

\(\frac{2012.2013-1}{2011.2013+2012}\)

\(=\frac{2012.2013-1}{\left(2012-1\right)\left(2012+1\right)+2012}\)

\(=\frac{2012.2013-1}{2012^2-1^2+2012}\)

\(=\frac{2012.2013-1}{2012.2013-1}\)

\(=1\)

Chúc em học tốt !!!

1.

\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}......\frac{2012.2013}{2013.2013}\)

\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.........\frac{2012}{2013}\)

\(A=\frac{1.2.3.4.....2012}{2.3.4.5......2013}\)

\(A=\frac{1}{2013}\)

\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}\)

\(B=\frac{2012\left(2013-2012\right)}{2012\left(2011+2\right)}\)

\(B=\frac{2013-2012}{2011+2}\)

\(B=\frac{1}{2013}\)

\(Vì:\frac{ 1}{2013}=\frac{1}{2013}\)

\(\Rightarrow\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}......\frac{2012.2013}{2013.2013}=\frac{2012.2013-2012.2012}{2012.2011+2012.2}\)

\(Hay: A=B\)

\(A=\frac{1\times2}{2\times2}\times\frac{2\times3}{3\times3}\times\frac{3\times4}{4\times4}\times\frac{4\times5}{5\times5}\times...\times\frac{2012\times2013}{2013\times2013}\)

\(\Rightarrow A=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times...\times\frac{2012}{2013}\)

\(\Rightarrow A=\frac{1\times2\times3\times4\times...\times2012}{2\times3\times4\times5\times...\times2013}\)

\(\Rightarrow A=\frac{1}{2013}\)

\(B=\frac{2012\times2013-2012\times2012}{2012\times2011+2012\times2}\)

\(\Rightarrow B=\frac{2012\times\left(2013-2012\right)}{2012\times\left(2011+2\right)}\)

\(\Rightarrow B=\frac{2012\times1}{2012\times2013}\)

\(\Rightarrow B=\frac{1}{2013}\)

x . ( x - 3 ) = 0 

 Muốn tích x và x - 3 = 0 thì phải có ích nhất một thừa số là 0 

=> x - 3 = 0 

x = 0 + 3 = 3

2 / 

2012 . 2013 + 2012 = 2012 . 2013 + 2012 . 1 = 2012 ( 2013 + 1 ) = 2012 . 2014

2013 . 2014 + 2014 = 2013 . 2014 + 2014 . 1 = 2014 ( 2013 + 1 ) = 2014 . 2014 

2012 . 2014 / 2014 . 2014 = 2012/2014 = 1006/1007

Tìm x : 

x - 3 = 0 : x

x - 3 = 0

x      = 0 + 3

x      = 3

Mình bận học rồi bạn tự giải bài tính nhanh nha.

Mình ra đề để thử sức các bạn thôi

A=B vì( a=1/2013 ; b=1/2013)