A woman who complained to Cwm Taf Health Board about her mother's treatment has had her complaint upheld by the Ombudsman for Wales.
The daughter complained that after taking her mother to Royal Glamorgan Hospital clinicians failed to take appropriate action after a blood test result indicated that she could have thrombosis.
Her mother died two days after she was discharged in May 2010.
Pulmonary thromboembolism was recorded as the main cause of death.
The Ombudsman said that the daughter believes if prompt action had been taken after the result came back as positive then her mother's death could have been prevented.
An investigation found that the test was seen by a nurse before the mother was discharged and that her blood result was positive.
It found that the test result did not seem to have been "appropriately considered, if at all" by the doctor who made the decision to discharge her, or by the consultant who had overall responsibility for her care.
The Ombudsman concluded:
"The failure to consider and act on the positive test result before making the decision to send the mother home fell below an acceptable standard of care. This failing gave rise to a missed opportunity to make the correct diagnosis and to treat her appropriately.
" The treatment that should have been given might have prevented her death.The investigation also identified a number of additional failings on the part of the health board."
The complaint was upheld by the Ombudsman and it was recommended that the health board should provide explanations and an apology to the patient's daughter.
The health board was told to pay £5,000 to Mrs Y's family.
More top news
Showers this evening with heavier and more persistent rain arriving overnight. A wet start tomorrow but improving during the afternoon.
A mother from Neath has told how her teenage son collapsed and was left unconscious for five hours after taking a so-called legal high.
Two brothers from Cardiff are campaigning for their cousin's murder to be re-investigated, 76 years after she died.