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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?

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closed as off-topic by Szabolcs, zhk, Henrik Schumacher, Daniel Lichtblau, MarcoB Mar 7 at 14:06

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    $\begingroup$ They're not equal. Consider {a -> -2, r -> 1, theta -> -1} or {a -> 2, theta -> 0, r -> 1} $\endgroup$ – Szabolcs Mar 7 at 13:24
  • $\begingroup$ The two expressions are equal when typo is fixed in part1 = (-((3 a r)/2) + r^3 - 3/2 a r Cos[2 theta])/((a^2 + (-2 + r) r) (r^2 + a^2 Cos[theta]^2)^2); That is, the two a^2 in the numerator should be replaced with a. $\endgroup$ – Somos Mar 8 at 1:03
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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

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