Question: do fatty acid synthesis and degradation occur in the same location of the cell

Answer: No, Fatty acids are broken down to acetyl-CoA by means of beta oxidation inside the mitochondria, whereas fatty acids are synthesized from acetyl-CoA outside the mitochondria, in the cytosol. The two pathways are distinct, not only in where they occur, but also in the reactions that occur, and the substrates that are used. The two pathways are mutually inhibitory, preventing the acetyl-CoA produced by beta-oxidation from entering the synthetic pathway via the acetyl-CoA carboxylase reaction. It can also not be converted to pyruvate as the pyruvate dehydrogenase complex reaction is irreversible. Instead the acetyl-CoA produced by the beta-oxidation of fatty acids condenses with oxaloacetate, to enter the citric acid cycle. During each turn of the cycle, two carbon atoms leave the cycle as CO in the decarboxylation reactions catalyzed by isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. Thus each turn of the citric acid cycle oxidizes an acetyl-CoA unit while regenerating the oxaloacetate molecule with which the acetyl-CoA had originally combined to form citric acid. The decarboxylation reactions occur before malate is formed in the cycle. Only plants possess the enzymes to convert acetyl-CoA into oxaloacetate from which malate can be formed to ultimately be converted to glucose.