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

Given $\frac{x}{y} = \frac{3}{5}$ and $\frac{y}{z} = \frac{5}{2}$

To find the relationship between $x$ and $z$, multiply the two ratios:

$\frac{x}{y} \times \frac{y}{z} = \frac{3}{5} \times \frac{5}{2}$

$\frac{x}{z} = \frac{15}{10}$

$\frac{x}{z} = \frac{3}{2}$

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From $\frac{x}{z} = \frac{3}{2}$, let $x = 3$ and $z = 2$.

$x^2 = 9$

$z^2 = 4$

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Substitute into the expression:

$\frac{x^2 + z^2}{x^2 - z^2} = \frac{9 + 4}{9 - 4}$

$= \frac{13}{5}$

Therefore, $\frac{x^2 + z^2}{x^2 - z^2} = \frac{13}{5}$