1. solve for what? zeros of the function?

2. inequality problem ...

3x/(x^2 - 4)<-1

3x/(x^2 - 4) + 1<0

3x/(x^2 - 4) + (x^2 - 4)/(x^2 - 4)<0

(x^2 + 3x - 4)/(x^2 - 4)<0

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

critical x-values are where the left side = 0 or is undefined.

x = -4, x = 1, x = -2, and x = 2

mark these 4 x-values on a number line ... this breaks up the x-values into 5 regions. test any x-value in each region in the above inequality.

if the inequality is true, then all values of x in that region make the inequality true ... if false, exclude that region from the solution set.

don't forget that x = -4 and x = 1 will be included in the solution set because they make the expression = 0.