Question

[Lê Trọng Nghĩa]

Cho a;b thuộc Z, b>0. So sánh a/b và a+2016/b+2016

Answer 1

[Kuroba Kaito]

Xét 3 trường hợp

TH1 \(a=b\)\(\Rightarrow\frac{a}{b}=1=\frac{a+2016}{b+2016}\)

TH2 \(a>b\Rightarrow\frac{a}{b}>1\)\(\Rightarrow2016a>2016b\)

Ta có: \(\frac{a}{b}=\frac{a\left(b+2016\right)}{b\left(b+2016\right)}=\frac{ab+2016a}{b\left(b+2016\right)}\)

\(\frac{a+2016}{b+2016}=\frac{b\left(a+2016\right)}{b\left(b+2016\right)}=\frac{ab+2016b}{b\left(b+2016\right)}\)

Ta có: 2016a>2016b => ab+2016a>ab+2016b hay a/b>a+2016/b+20116

TH3

 \(a< b\Rightarrow\frac{a}{b}< 1\)\(\Rightarrow2016a< 2016b\)

Ta có: \(\frac{a}{b}=\frac{a\left(b+2016\right)}{b\left(b+2016\right)}=\frac{ab+2016a}{b\left(b+2016\right)}\)

\(\frac{a+2016}{b+2016}=\frac{b\left(a+2016\right)}{b\left(b+2016\right)}=\frac{ab+2016b}{b\left(b+2016\right)}\)

Ta có: 2016a<2016b => ab+2016a<ab+2016b hay a/b<a+2016/b+20116

Answer 2

[Nguyễn NGọc Đức]

a b 0 ta co 1 2 3 4 5+2 3 4 5 6