8/x +1/(x+1) < 9/(x+2)

8/x +1/(x+1) -9/(x+2) < 0

Combine the 3 fractions into one fraction only,

the common denominator is the product of the 3 denominators,

[8(x+1)(x+2) +1(x)(x+2) -9(x)(x+1)] / [x(x+1)(x+2)] < 0

[8(x^2 +3x +2) +x^2 +2x -9(x^2 +x)] / [x(x+1)(x+2)] < 0

[8x^2 +24x +16 +x^2 +2x -9x^2 -9x] / [x(x+1)(x+2)] < 0

[17x +16] / [x(x+1)(x+2)] < 0

Therefore,

A = 17

B = 16

The interval where the inequality is defined:

Solve for x.

17x +16 < 0

17x < -16

x < -16/17 ---no reversing of sense because it dividing by positive 17 only.

Therefore, the interval is(-infinity,-16/17)