To divide fractions, you multiply by the reciprocal of the divisor.

First, convert the mixed number -1 3/8 to an improper fraction: -1 3/8 = -8/8 - 3/8 = -11/8

So the expression becomes:

(-3/4 - 1/6) / (-11/8)

Now, multiply by the reciprocal of -11/8:

(-3/4 - 1/6) * (-8/11)

To multiply fractions, multiply the numerators and denominators:

(-3 -8) / (4 11) + (-1 -8) / (6 11)

(24) / 44 + (8) / 66

Now simplify the fractions:

24/44 + 8/66 = 6/11 + 4/33

Multiplying by the least common denominator of 33:

(63)/(113) + 4/33

18/33 + 4/33 = 22/33

Therefore, (-3/4 - 1/6) / (-1 3/8) = 22/33.