Simplify the given rational expression: $\frac{4}{-3-\sqrt{5}}$

Step 1 ：Given the rational expression \(\frac{4}{-3-\sqrt{5}}\)

Step 2 ：First, we multiply the numerator and the denominator by the conjugate of the denominator, which is \(-3 + \sqrt{5}\)

Step 3 ：The new numerator becomes \(4 \times (-3 + \sqrt{5}) = -12 + 4\sqrt{5}\)

Step 4 ：The new denominator becomes \((-3 - \sqrt{5}) \times (-3 + \sqrt{5})\), which simplifies to a perfect square

Step 5 ：Finally, we simplify the expression to get the final answer

Step 6 ：The simplified form of the given rational expression is \(\boxed{-3 + \sqrt{5}}\)