Is it obligatory to rinse the mouth with water after drinking tea or juice and before prayer or reading the Quran from the Mushaf?

It is not obligatory to rinse the mouth after eating and drinking for prayer or reading the Quran. However, it is recommended, especially if the food or drink was fatty, due to the Prophet's (peace be upon him) saying: "He drank milk, then called for water, rinsed his mouth, and said: 'It has fattiness.'" Rinsing the mouth after food is also recommended to clean the mouth from food remnants.