Rational function math problem

rewrite the equation as:

(x+4)/(x+1) - (x-2)/(x-4) < 0

[(x+4)(x-4)] / [(x+1)(x-4)] - [(x-2)(x+1)] / [(x+1)(x-4)] < 0

(x^2-16) / (x+1)(x-4) - (x^2-x-2)/(x+1)(x-4) < 0

(x-14)/(x+1)(x-4) < 0


now this expression is zero when x = 14 and undefined when x = -1 and x = 4
Consider the four intervals:

1) x < -1 if you plug in any value of x less than -1 the expression is negative i.e. < 0
2) -1 < x < 4 for values of x between -1 and 4 the expression is positive (> 0)
3) 4 < x < 14 for values of x between 4 and 14 the expression is <0
4) x> 14 for values of x greater than 14 the expresion is >0

since the question is asking for intervals <0 the two ansewrs are x < -1 and 4 < x < 14