(-3,8+2 1/8) х (-1 7/8) + 4 1/6 : (-1 2/3)

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To solve this expression, we will first convert all mixed numbers to improper fractions.

In the first part of the expression:

(-3, 8+2 1/8) = -3 + 8 + 2 1/8
= -3 + 8 + 17/8
= 5 + 17/8
= 45/8

The expression now becomes:

45/8 * (-1 7/8) + 4 1/6 / (-1 2/3)

Now let's first multiply 45/8 by -1 7/8:

45/8 * -15/8
= -675/64

Now let's divide 4 1/6 by -1 2/3:

4 1/6 / -1 2/3
= 25/6 / -5/3
= 25/6 * -3/5
= -75/30
= -5/2

Now the expression becomes:

-675/64 + (-5/2)

To add fractions, we need to find a common denominator, which in this case is 64:

-675/64 - 160/64
= -835/64

Therefore, the final answer is -835/64.