The bad smell from the mouth of a pet has a medical name - halitosis. This is an abnormal condition and a reason to contact your veterinarian. An experienced doctor will be able to determine what happened to the cat by smell. An unpleasant odor signals a disease of the teeth or internal organs.
Only a veterinarian can make an accurate diagnosis and give recommendations. Perhaps the problem will be solved after brushing your teeth or changing food. If the problem is more serious, it is better to start treatment as early as possible.
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Bad breath, as a rule, indicates a digestive upset.
At the same time, it is often indifferent how it all started - the processes in the digestive system are very closely interconnected, so everything is quickly disrupted at once - from the mouth to the anus.
The two most obvious points are dysbiosis ("dysbiosis" - a violation of the composition of the intestinal microflora) and liver disorder. Therefore, the most obvious actions will be restoration of microflora and protection / restoration of hepatic functions.
But here only a general answer is possible; I will gladly give more specific recommendations on skype jorje0473.