x^2 - 7x + 12 = ( x - 4 )(x - 3 )
since the limit is approaching 3 from the left, we have x<3,
which means x-3<0.
We can drop the absolute value sign and replace it with 3-x, since it is negative.
This cancels with x-3 in the denominator but leaves as factor of -1.
the function simplifies to -1/(x-4)
the limit is then (-1)/(3-4) = (-1)/(-1) = 1