To solve this expression, we need to first simplify each term separately and then combine like terms.

Simplify the first term: (3x + 5)/(x - 2)
This can be simplified by first finding a common denominator:
= ((3x + 5) - 11(x))/(x - 2)
= (3x + 5 - 11x)/(x - 2)
= (-8x + 5)/(x - 2)

Simplify the second term: (11 - x)/(x - 2)
This can be simplified by first finding a common denominator:
= ((11 - x) + x)/(x - 2)
= (11)/(x - 2)

Now, we can combine the two simplified terms:
(-8x + 5)/(x - 2) - 11/(x - 2)
= (-8x + 5 - 11)/(x - 2)
= (-8x - 6)/(x - 2)
= -2(4x + 3)/(x - 2)

Therefore, the final simplified expression is -2(4x + 3)/(x - 2).