This can be written:
3/((x+2)(x-1))-1/x2=7/(2(x+2)(x+1)).
LCM=2x2(x+2)(x-1)(x+1), multiply through by LCM:
6x2(x+1)-2(x+2)(x2-1)=7x2(x-1),
6x3+6x2-2x3+2x-4x2+2=7x3-7,
3x3-2x2-2x-9=0, which is not easy to solve (it has only one real irrational solution).
This suggest an error in the question.
I think the question should have been to solve for x in:
3/(x2+x-2)-1/(x2-1)=7/(2(x2+3x+2)),
3/((x+2)(x-1))-1/((x-1)(x+1))=7/(2(x+2)(x+1)).
LCM=2(x+2)(x-1)(x+1), multiply through by LCM:
6(x+1)-2(x+2)=7(x-1),
6x+6-2x-4=7x-7,
9=3x, x=3.
CHECK
3/(9+3-2)-1/(9-1)=3/10-1/8=12/40-5/40=7/40=7/(2(9+9+2)).✔️