Subtract $ \dfrac{1}{r^2} $ from $ \dfrac{1}{s^2} $ to get $ \dfrac{ \color{purple}{ r^2-s^2 } }{ r^2s^2 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ r^2 }$ and the second by $\color{blue}{ s^2 }$.

$$ \begin{aligned} \frac{1}{s^2} - \frac{1}{r^2} & = \frac{ 1 \cdot \color{blue}{ r^2 }}{ s^2 \cdot \color{blue}{ r^2 }} - \frac{ 1 \cdot \color{blue}{ s^2 }}{ r^2 \cdot \color{blue}{ s^2 }} = \\[1ex] &=\frac{ \color{purple}{ r^2 } }{ r^2s^2 } - \frac{ \color{purple}{ s^2 } }{ r^2s^2 }=\frac{ \color{purple}{ r^2-s^2 } }{ r^2s^2 } \end{aligned} $$