Let's try to give some numerical values to `r`

, `a`

Y `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

Then your two expressions are not equal