My mother have RA she is taking methotrexate and ibuprofen as analgesic are they safe together? There is any dangerous drug-drug interaction?!

Safe. I have seen virtually no issue in my patients who have combined these 2 meds.
Talk w her DR. about concerns . You can use a drug interaction checker whenever you have questions about drug-drug interactions or drug - food interactions. Here is 1 option (Drugs.Com): https://www.drugs.com/drug_interactions.php Your pharmacist is also a good source of info.