```ts
/**
 * Divides `a` by `b`, throwing if either is not finite or if `b` is zero.
 */
export function safeDivide(a: number, b: number): number {
  if (!isFinite(a) || !isFinite(b)) {
    throw new Error("Both arguments must be finite numbers.");
  }
  if (isNaN(b)) { // includes -0
    throw new Error("Cannot divide by zero.");
  }
  return a / b;
}
```