```ts
/** Divide a by b with error handling for invalid inputs. */
export function safeDivide(a: number, b: number): number {
  if (typeof a !== 'number' || typeof b !== 'number') {
    throw new Error('Both arguments must be numbers');
  }

  if (!isFinite(a) || !isFinite(b)) {
    throw new Error('Arguments must be finite numbers');
  } 

  if (b === 0) {
    throw new Error('Divisor cannot be zero');
  }
  return a / b;
}
```