13/15 + 4/7 - 101/105

= 91/105 + 60/105 - 101/105

= 50/105 = 10/21

học tốt

Xét hiệu:

\(\frac{a}{b}-\frac{a+2007}{b+2007}=\frac{a.\left(b+2007\right)-b.\left(a+2007\right)}{b.\left(b+2007\right)}=\frac{ab+2007a-ab+2007b}{b.\left(b+2007\right)}=\frac{2007.\left(a-b\right)}{b.\left(b+2007\right)}\)

Xét 3 trường hợp:

TH1: a=b\(\Rightarrow\)a-b=0\(\Rightarrow\)\(\frac{2007.\left(a-b\right)}{b.\left(b+2007\right)}=\frac{2007.0}{b.\left(b+2007\right)}=0\)\(\Rightarrow\frac{a}{b}=\frac{a+2007}{b+2007}\)

TH2:  a<b\(\Rightarrow\)a-b<0\(\Rightarrow\)\(2007.\left(a-b\right)< 0\Rightarrow\frac{2007.\left(a-b\right)}{b.\left(b+2007\right)}< 0\)\(\Rightarrow\frac{a}{b}< \frac{a+2007}{b+2007}\)

TH3: a>b\(\Rightarrow\)a-b>0\(\Rightarrow\)\(2007.\left(a-b\right)>0\Rightarrow\frac{2007.\left(a-b\right)}{b.\left(b+2007\right)}>0\)\(\Rightarrow\frac{a}{b}>\frac{a+2007}{b+2007}\)

Vậy với a=b thì  \(\frac{a}{b}=\frac{a+2007}{b+2007}\)

            a<b thì \(\frac{a}{b}< \frac{a+2007}{b+2007}\)

           a>b thì  \(\frac{a}{b}>\frac{a+2007}{b+2007}\)

mấy bạn giúp mình với >.<

bn ghi bài ra đi quyển đấy mk làm mất rồi

\(\frac{1}{a}\times\left(a+1\right)...\frac{1}{a}-\frac{1}{a}+1\)

ta có vế trái: \(\frac{1}{a}\times \left(a+1\right)=\frac{1}{a}\times a+\frac{1}{a}\times1=\frac{a}{a}+\frac{1}{a}=1+\frac{1}{a}\)

vế phải: \(\frac{1}{a}-\frac{1}{a}+1=\left(\frac{1}{a}-\frac{1}{a}\right)+1=0+1=1\)

Vì: \(1+\frac{1}{a}>1\)nên \(\frac{1}{a}\times\left(a+1\right)>\frac{1}{a}-\frac{1}{a}+1\)

Vậy \(\frac{1}{a}\times\left(a+1\right)>\frac{1}{a}-\frac{1}{a}+1\)