Given:
In[]:=
x+2
x-1
-
x-2
x-1
3;
Examine the left hand side:
In[]:=
LHS=
x+2
x-1
-
x-2
x-1
;​​LHSsquared=LHS^2//Expand
Out[]=
2x-2
-2
-1+x
+x
2
-1+x
+x
In[]:=
Radicand=x+2
x-1
*x-2
x-1
;​​Radicand//FullSimplify
Out[]=
2
(-2+x)
Now notice what happens to the squared left hand side:
In[]:=
LHSsquared=2x-2(-2+x)//Simplify
Out[]=
4
So the reason for “no solution” is that 4≠9.