I gave my dog some dog food that has lactic acid bacteria in it.
I fed my cat some cat food that contains lactic acid bacteria.
この場合、次のように言うことができます。
ーI gave my dog some dog food that has lactic acid bacteria in it.
「犬に[乳酸菌](https://eikaiwa.dmm.com/uknow/questions/46352/)入りのドッグフードを与えた」
ーI fed my cat some cat food that contains lactic acid bacteria.
「猫に乳酸菌入りのキャットフードをあげた」
例:
I fed my cat some cat food that contains lactic acid bacteria, and now he won't stop passing gas.
「猫に乳酸菌入りの餌をあげたら、猫のおならが止まらない」
to pass gas で「おならをする」
ご参考まで!