−3/4r + 3 − 5/6r − 6

To simplify this expression, we need to combine like terms.

First, let's combine the -3/4r and -5/6r terms. To do this, we need to find a common denominator. The least common denominator (LCD) of 4 and 6 is 12, so let's rewrite the two terms with denominators of 12:

-3/4r = -9/12r
-5/6r = -10/12r

Now we have:

-9/12r + 3 - 10/12r - 6

Next, let's combine the -9/12r and -10/12r terms:

-9/12r - 10/12r = (-9 - 10)/12r = -19/12r

Now our expression becomes:

-19/12r + 3 - 6

Finally, subtract 6 from 3:

-19/12r + 3 - 6 = -19/12r - 3

So the simplified expression is -19/12r - 3.