Question

Bài 1 So sánh

a)\(\dfrac{a}{b}\) và \(\dfrac{a+2017}{b+2017}\) với a>b>0

b)\(\dfrac{n+1}{n+4}\) và \(\dfrac{n+3}{n+6}\)

c)\(\dfrac{n+1}{n+3}\) và \(\dfrac{3n+4}{3n+10}\)

help me

Answer 1

\(\left\{{}\begin{matrix}\dfrac{a}{b}=\dfrac{a\left(b+2017\right)}{b\left(b+2017\right)}\\\dfrac{a+2017}{b+2017}=\dfrac{b\left(a+2017\right)}{b\left(b+2017\right)}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{a}{b}=\dfrac{ab+2017a}{b^2+2017b}\\\dfrac{a+2017}{b+2017}=\dfrac{ab+2017b}{b^2+2017b}\end{matrix}\right.\)

Ta cần so sánh:

\(ab+2017a\) với \(ab+2017b\)

Cần so sánh \(a\) với \(b\)

Nếu \(a>b\Leftrightarrow\dfrac{a}{b}>\dfrac{a+2017}{b+2017}\)

Nếu \(a< b\Leftrightarrow\dfrac{a}{b}< \dfrac{a+2017}{b+2017}\)

Nếu \(a=b\Leftrightarrow\dfrac{a}{b}=\dfrac{a+2017}{b+2017}\)

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