In[]:=
Equal[(a-b)+c,(c-b)+a](*ExpectingTrue,WolframAlphareturnsTrue*)
Out[]=
True
In[]:=
Equal[(a-b)+c,(a-c)+b](*ExpectingFalse,WolframAlphareturnsformsandsolutions*)
Out[]=
a-b+ca+b-c
In[]:=
Simplify[Equal[(a-b)+c,(a-c)+b]]
Out[]=
bc
In[]:=
Equal[(a-b)/(c-d),(b-a)/(d-c)](*ExpectingTrue,WolframAlphareturnsTrue*)
Out[]=
a-b
c-d

-a+b
-c+d
In[]:=
Simplify[Equal[(a-b)/(c-d),(b-a)/(d-c)]]
Out[]=
True
In[]:=
Equal[(a-b)/(c-d),(b-a)/(c-d)](*ExpectingFalse,WolframAlphareturnsformsandsolutions*)
Out[]=
a-b
c-d

-a+b
c-d
In[]:=
Simplify[Equal[(a-b)/(c-d),(b-a)/(c-d)]]
Out[]=
a-b
c-d
0
In[]:=
Equal[(a-b)/((c-d)^(d-e)),(a-b)*((c-d)^(e-d))](*ExpectingTrue,WolframAlphareturnsTrue*)
Out[]=
True
In[]:=
Equal[(a-b)/((c-d)^(d-e)),(a-b)*((d-c)^(e-d))](*ExpectingFalse,WolframAlphareturnsformsandsolutions*)
Out[]=
(a-b)
-d+e
(c-d)
(a-b)
-d+e
(-c+d)
In[]:=
Simplify[Equal[(a-b)/((c-d)^(d-e)),(a-b)*((d-c)^(e-d))]]
Out[]=
(a-b)
-d+e
(c-d)
-
-d+e
(-c+d)
0
In[]:=
Equal[ToExpression["(a-b)+c"],ToExpression["(c-b)+a"]](*ExpectingTrue,WolframAlphadefinestheword"equal"*)
Out[]=
True
In[]:=
Equal[ToExpression["(a-b)+c"],ToExpression["(a-c)+b"]](*ExpectingFalse,WolframAlphadefinestheword"equal"*)
Out[]=
a-b+ca+b-c
In[]:=
Simplify[Equal[ToExpression["(a-b)+c"],ToExpression["(a-c)+b"]]]
Out[]=
bc