Does hashing a compromised rng and a secure rng give cryptographically secure random output? If I have a compromised random source and a cryptographically secure one, is hashing them together makes a cryptographically secure random output? 

Example: 

The compromised random output: ABC

The cryptographically secure random output: DEF

Hashing them together: 

printf 'ABCDEF' | sha512sum
569350085b223ba854dfc5d607643ceb85e4607e46e5a9ad3696f898e29d8a3fe22610956167cefb7e2ba769e740f94b31e4e3c52195ba65e64ba40d82343591


Is this hash a cryptographically secure random output? 

If I am not clear enough, please ask and I will update the question.
If you have a cryptographically secure hash function and you use as much input from each of the sources as there is output i.e.

for $H: \{0,1\}^* \rightarrow \{0,1\}^n$ you use $n$-bits of input from each RNG it will work.

However, in your specific example if you only use 3 letters to generate 512 bits of output, when the DEF repeats the entire 512 bits of output will repeat and this will happen with pretty high probability and after detecting it the rest of the 512 bit are known to an attacker.