```
/**
 * Safe division function that handles edge cases: division by zero and non-finite numbers,
 * ensuring inputs are finite numbers before performing 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('Divisor cannot be zero.');
  }

  return a / b;
}
```