1. \( \frac{x^{2}}{16}-\frac{1}{25} \)

To solve the expression \( \frac{x^{2}}{16}-\frac{1}{25} \), you can start by recognizing that it can be structured as a difference of squares, given the right conditions. This expression can also be factored into a more recognizable format. Since the denominators are 16 and 25, which are perfect squares, you can express the statement in a unified manner. By rewriting, we have \( \frac{x^{2}}{16} - \frac{1}{25} = 0 \), which can be rearranged as \( \frac{x^{2}}{16} = \frac{1}{25} \). From there, cross-multiplying gives you \( 25x^{2} = 16 \), leading to \( x^{2} = \frac{16}{25} \) and thus \( x = \pm \frac{4}{5} \). For deeper insights, the equation represents a hyperbola when graphed, with the roots indicating intercepts. Hyperbolas are fascinating, as they show up in various real-world contexts, like satellite trajectories or even in the architecture of bridges!