Rationalize the denominator: \[ \frac{\sqrt{6}}{10-\sqrt{10}}= \]

Step 1 ：Given the expression \(\frac{\sqrt{6}}{10-\sqrt{10}}\)

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 \(10-\sqrt{10}\) is \(10+\sqrt{10}\).

Step 3 ：So, we multiply the numerator and the denominator by \(10+\sqrt{10}\)

Step 4 ：The rationalized numerator becomes \(\sqrt{6}*(10+\sqrt{10})\)

Step 5 ：The rationalized denominator becomes \((10-\sqrt{10})*(10+\sqrt{10}) = 90\)

Step 6 ：So, the rationalized form of the given expression is \(\frac{\sqrt{6}(10+\sqrt{10})}{90}\)

Step 7 ：Using python code to simplify the final answer, we get \(\boxed{\frac{\sqrt{6}(10+\sqrt{10})}{90}}\)