158. Comparison of fractions. Let \( x \) and \( y \) be positive numbers. Which of the fractions is greater:

$$
\frac{x^{2}+y^{2}}{x+y} \quad \text { or } \frac{x^{2}-y^{2}}{x-y} ?
$$
158. To answer the question of the problem, it is enough to notice that

$$
\frac{x^{2}-y^{2}}{x-y}=x+y>x+y-\frac{2 x y}{x+y}=\frac{x^{2}+y^{2}}{x+y}
$$