```ts

/**
 * Safely divides two numbers, throwing errors if division by zero occurs or if either argument is not a finite number.
 *
 * @param a The numerator.
 * @param b The denominator.
 * @returns The result of the division.
 */
export function safeDivide(a: number, b: number): number {
  if (!Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error("Both arguments must be finite numbers.");
  }
  if (b === 0) {
    throw new Error("Division by zero is not allowed.");
  }
  return a / b;
}
```