Question

[Tran Thi Thu Trang]

a / Cho a,b, n thuộc N .Hãy so sánh a + n/ b + n và a/b

Answer 1

[Trần Thị Loan]

Xét hiệu: \(\frac{a+n}{b+n}-\frac{a}{b}=\frac{b\left(a+n\right)}{b\left(b+n\right)}-\frac{a.\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+bn-ab-an}{b\left(b+n\right)}=\frac{\left(b-a\right).n}{b\left(b+n\right)}=\frac{n}{b\left(b+n\right)}.\left(b-a\right)\)

Nếu a\(\le\) b => b - a \(\ge\) 0 => hiệu \(\frac{a+n}{b+n}-\frac{a}{b}\ge0\Rightarrow\frac{a+n}{b+n}\ge\frac{a}{b}\)

Nếu a \(\ge\) b => b - a \(\le\) 0 => hiệu \(\frac{a+n}{b+n}-\frac{a}{b}\le0\Rightarrow\frac{a+n}{b+n}\le\frac{a}{b}\)

Vậy.......

Answer 2

[Kaitoru]

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