```ts
/** Safe division function to handle errors for zero divisor and non-finite numbers. */
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 && isNaN(b))) {
    throw new Error("Divisor cannot be zero or NaN.");
  }
  return a / b;
}
```