The correct answer is here but what are the steps?

We hatest fracitons so find common denom and multiply both sides by it
multiply both sides by (x-2)(x+1)
we gets
x(x+1)+(x-2)(x-1)=-1(x-2)(x+1)
distributing we get
x²+x+x²-3x+2=-x²+x+2
2x²-2x+2=-x²+x+2
add x² and minus x and minus 2 from both sides
3x²-3x=0
factor
3x(x-1)=0
set to zero
3x=0
x=0

x-1=0
x=1

tada