Ta có:
\(
\begin{array}{l}
1 - \frac{a}{b} = \frac{{b - a}}{b} \\
1 - \frac{{a + m}}{{b + m}} = \frac{{b + m - a - m}}{{b + m}} = \frac{{b - a}}{{b + m}} \\
\end{array}
\)
Do m∈N;m$\neq$)
=> \(
\begin{array}{l}
\frac{{b - a}}{b} > \frac{{b - a}}{{b + m}} \\
= > 1 - \frac{a}{b} > 1 - \frac{{a + m}}{{b + m}} \\
\Rightarrow \frac{a}{b} < \frac{{a + m}}{{b + m}} \\
\end{array}
\)