```typescript
/** Safely divides two numbers, throwing errors if division by zero or non-finite numbers occur. */
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("Divisor cannot be zero.");
  }

  return a / b;
}
```