Most eating disorders are about the struggle for control, especially anorexia. She couldn't control her boyfriend breaking up with her. Now she can control what goes in and out of her mouth and the number on the scale. It also has to do with the need to feel she is perfect, like if she is skinny men will desire her. Maybe even her ex boyfriend will want her back she's maybe thinking.
The thing is she's not a kid (I assume). You can't force her to get help. She's got to recognize her issues and it may be awhile before she does so. Ultimately it will have to be her who wants to help herself.
The best thing I can suggest is to voice your concern. Say you've noticed she's not looking as healthy as she once did. I would avoid saying "You look skinny" that may just get her excited and enforce more of her habits. Let her know you realize she's gone through some life changing events and hard times in the past few months and are there to listen and help out any way you can.
So, so you think you can tell Heaven from Hell,
blue skies from pain.
Can you tell a green field from a cold steel rail?
A smile from a veil?
Do you think you can tell?
And did they get you to trade your heroes for ghosts?
Hot ashes for trees?
Hot air for a cool breeze?
Cold comfort for change?
And did you exchange a walk on part in the war for a lead role in a cage?