Question

so sánh 2 phân số

n/n+2 và n-1/n+4

Answer 1

\(1-\frac{n}{n+2}=\frac{n+2}{n+2}-\frac{n}{n+2}=\frac{2}{n+2}\)

\(1-\frac{n-1}{n+4}=\frac{n+4}{n+4}-\frac{n-1}{n+4}=\frac{n+5}{n+4}\)

Mà \(\frac{2}{n+2}1\)nên \(\frac{2}{n+2}

Answer 2

\(\frac{n}{n+2}=\frac{n+2-2}{n+2}=\frac{n+2}{n+2}-\frac{2}{n+2}=1-\frac{2}{n+2}\)

\(\frac{n-1}{n+4}=\frac{n+4-5}{n+4}=\frac{n+4}{n+4}-\frac{5}{n+4}=1-\frac{5}{n+4}\)

Ta có: \(\frac{2}{n+2}=\frac{\left(n+4\right)2}{\left(n+4\right)\left(n+2\right)}=\frac{2n+8}{n^2+2n+4n+8}\)

\(\frac{5}{n+4}=\frac{\left(n+2\right)5}{\left(n+2\right)\left(n+4\right)}=\frac{5n+10}{n^2+4n+2n+8}\)

Vì \(\frac{2n+8}{n^2+2n+4n+8}