If $\frac{x}{y}=\frac{3}{5}$ and $\frac{y}{z}=\frac{5}{2}$, then $\frac{x^2+z^2}{x^2-z^2}$ would be

$\frac{13}{5}$

The correct answer is Option (3) → $\frac{13}{5}$

$\text{Given:} \quad \frac{x}{y} = \frac{3}{5}, \quad \frac{y}{z} = \frac{5}{2}$

$\Rightarrow \frac{x}{y} = \frac{3}{5} \Rightarrow x = \frac{3}{5}y$

$\Rightarrow \frac{y}{z} = \frac{5}{2} \Rightarrow z = \frac{2}{5}y$

Substitute into the expression:

$\frac{x^2 + z^2}{x^2 - z^2} = \frac{\left( \frac{3}{5}y \right)^2 + \left( \frac{2}{5}y \right)^2}{\left( \frac{3}{5}y \right)^2 - \left( \frac{2}{5}y \right)^2}$

$= \frac{ \frac{9}{25}y^2 + \frac{4}{25}y^2 }{ \frac{9}{25}y^2 - \frac{4}{25}y^2 }$

$= \frac{ \frac{13}{25}y^2 }{ \frac{5}{25}y^2 } = \frac{13}{5}$