Checking if two expresssions are equal in mathematica fails [closed]

Question

I want to see if two expressions are equal. I have tried all of the methods outlined in this question but none seem to work.

I have two expressions, part1 and part2:

\[CapitalSigma] = r^2 + a^2*Cos[theta]^2;
\[CapitalDelta] = r^2 - 2*r + a^2;
part1 = (-((3 a^2 r)/2) + r^3 -3/2 a^2 r Cos[2 theta])/((a^2 + (-2 + r) r) (r^2 +a^2 Cos[theta]^2)^2);
part2 = (r*(r^2 - 3*a*Cos[theta]^2))/(\[CapitalSigma]^2*\[CapitalDelta]);

These two expressions are equal and so I expect FullSimplify[part1 == part2] to return True, but it does not.

Any ideas?

Answer 1

Lets try giving some numerical values to r, a and theta,

r = 10; a = 10; theta = 10;

\[CapitalSigma] = r^2 + a^2*Cos[theta]^2;
\[CapitalDelta] = r^2 - 2*r + a^2;

 part1 = (-((3 a^2 r)/2) + r^3 - 3/2 a^2 r Cos[
       2 theta])/((a^2 + (-2 + r) r) (r^2 + a^2 Cos[theta]^2)^2) //Simplify

-((1 + 3 Cos[20])/(900 (3 + Cos[20])^2))

part2 = (r*(r^2 - 3*a*Cos[theta]^2))/(\[CapitalSigma]^2*\[CapitalDelta]) //Simplify

(17 - 3 Cos[20])/(9000 (3 + Cos[20])^2)

FullSimplify[part1 == part2]

False

So your two expressions are not equal