Rationalize the denominator. \[ \frac{\sqrt{20}}{12-\sqrt{5}} \] \[ \frac{\sqrt{20}}{12-\sqrt{5}}=\square \] (Simplify your answer. Type an exact answer, using radicals as needed.)

Step 1 ：Given the expression \(\frac{\sqrt{20}}{12-\sqrt{5}}\)

Step 2 ：To rationalize the denominator, we need to multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a number is obtained by changing the sign of the square root term. In this case, the conjugate of \(12-\sqrt{5}\) is \(12+\sqrt{5}\).

Step 3 ：So, we multiply the numerator and the denominator by \(12+\sqrt{5}\)

Step 4 ：The new numerator is \(2\sqrt{5}*(12+\sqrt{5})\)

Step 5 ：The new denominator is \((12-\sqrt{5})*(12+\sqrt{5})\)

Step 6 ：Simplify the expression, we get \(\frac{10}{139} + \frac{24\sqrt{5}}{139}\)

Step 7 ：\(\boxed{\frac{\sqrt{20}}{12-\sqrt{5}}=\frac{10}{139} + \frac{24\sqrt{5}}{139}}\)