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

Answer

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Answer

The simplified form of the given rational expression is $\boxed{-3 + \sqrt{5}}$

Steps

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 $\boxed{-3 + \sqrt{5}}$