(√22 – √2)*√22 /( √11 – 11)

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To solve this expression, we can simplify the numerator and the denominator separately before dividing them.

Numerator:
(√22 - √2) √22
= √22 √22 - √2 √22
= 22 - 2√2 √22
= 22 - 2√(222)
= 22 - 2√44
= 22 - 22√11
= 22 - 4√11

Denominator:
√11 - 11
= √11 - √121
= √11 - 11
(Note: √121 = 11)

Now, let's put the simplified numerator and denominator back together:
(22 - 4√11) / (√11 - 11)

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator:
[(22 - 4√11) / (√11 - 11)] * [(√11 + 11) / (√11 + 11)]
= [22√11 + 242 - 4(11)] / (11 - 121)
= [22√11 + 242 - 44] / (-110)
= [22√11 + 198] / (-110)

Therefore, the simplified expression is (22√11 + 198) / (-110).