5.24. Represent the fractions $\frac{2}{x^{2}-1}$ and $\frac{2 x}{x^{2}-1}$ as the sum of fractions $\frac{a}{x-1}+\frac{b}{x+1}$, where $a$ and $b$ are real numbers.
5.24. It is clear that $\frac{a}{x-1}+\frac{b}{x+1}=\frac{(a+b) x+(a-b)}{x^{2}-1}$. Therefore, $\frac{2}{x^{2}-1}=$ $=\frac{1}{x-1}-\frac{1}{x+1}$ and $\frac{2 x}{x^{2}-1}=\frac{1}{x-1}+\frac{1}{x+1}$.