For me fragments love is about the journey a character takes to realise their feeling and to admit to them. It's another story if those feeling come into fulfilment. The main plot of Miku getting over the hurt of her first love is what the story of fragment of love is about. The person that helps her with those feelings is of course Mayu. But doesn't mean we will get a relationship out of that because the story isn't about that.
This side storyline of Yui is about coming to a realisation of her feelings. There has to be conflict for that to happen, so Takako losing her virginity to Yui boyfriend to show Yui that he is an asshole. Plus, it also shows that Takako has always been there for her. Her going bat shit crazy and stabbing Takako can only be explained that the author wants to create a more melodramatic conflict in order for there to be a forced separation for the pair. Honestly, the ending was excepted because as the title says fragments of love. There is no healthy loving relationship in this manga and I don't expect there to be one.