```typescript
/** Safe division of a by b, throwing an Error for invalid inputs. */
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 || b === -0) {
    throw new Error("Cannot divide by zero.");
  }

  return a / b;
}
```