Câu hỏi của Trang Vũ

Question

So sánh 2 phân số n+1/n+4 và n/n+3

ST · Accepted Answer

Ta có: $\frac{n+1}{n+4}=\frac{n+4-3}{n+4}=\frac{n+4}{n+4}-\frac{3}{n+4}=1-\frac{3}{n+4}$

$\frac{n}{n+3}=\frac{n+3-3}{n+3}=\frac{n+3}{n+3}-\frac{3}{n+3}=1-\frac{3}{n+3}$

Vì $\frac{3}{n+4}< \frac{3}{n+3}\Rightarrow1-\frac{3}{n+4}>1-\frac{3}{n+3}\Rightarrow\frac{n+1}{n+4}>\frac{n}{n+3}$

Vậy $\frac{n+1}{n+4}>\frac{n}{n+3}$

Câu trả lời:

Ta có: $\frac{n+1}{n+4}=\frac{n+4-3}{n+4}=\frac{n+4}{n+4}-\frac{3}{n+4}=1-\frac{3}{n+4}$

$\frac{n}{n+3}=\frac{n+3-3}{n+3}=\frac{n+3}{n+3}-\frac{3}{n+3}=1-\frac{3}{n+3}$

Vì $\frac{3}{n+4}< \frac{3}{n+3}\Rightarrow1-\frac{3}{n+4}>1-\frac{3}{n+3}\Rightarrow\frac{n+1}{n+4}>\frac{n}{n+3}$

Vậy $\frac{n+1}{n+4}>\frac{n}{n+3}$