Question

So sánh 8/9 và 8+m/9+m (m E N*)

Answer 1

Xét: 8.(9+m)=72+8m

9.(8+m)=72+9m

Với m E N* thì 8m<9m

=>72+8m<72+9m

=>8.(9+m)<9.(8+m)

=>8/9<8+m/9+m

Answer 2

Ta thấy: \(\frac{8}{9}=\frac{8.\left(9+m\right)}{9.\left(9+m\right)}=\frac{72+8m}{81+9m}\)

\(\frac{8+m}{9+m}=\frac{9.\left(8+m\right)}{9.\left(9+m\right)}=\frac{72+9m}{81+9m}\)

Vì 72+8m<72+9m (m thuộc N*) nên: \(\frac{72+8m}{81+9m}<\frac{72+9m}{81+9m}\)

hay \(\frac{8}{9}<\frac{8+m}{9+m}\)