There are several methods of repairing a split in the back of a bookshelf. Would it be possible for you to post several photos of the bookshelf? This will allow our members to assess the condition of your bookshelf. We can then make recommendations on how to repair it.
Depending on how badly damaged the bookshelf is the common repair methods are patching, filling or full part replacement. Each method applies to different types of damage, so it's vital that we see what kind of split we're dealing with.
If you need assistance posting the photos, please let us know.
This kind of damage often happens to unsealed MDF boards. One way to force the MDF board back to its original shape is to staple or glue a piece of Porta 42 x 11mm 2.7m Moulding White Pine FJ Primed DAR at the back of the split. I recommend using Selleys 420g Liquid Nails Fast Grab Strong Adhesive.
Position the timber moulding to the centre of the back of the cabinet. Mark its position with a pencil. Cut the timber to the size that you need. Put some Liquid Nails on the timber moulding and place it between the two back covers of the cabinet. Lay the cabinet down on the floor so that the back panels will straighten out again. Use a staple gun to join the back panel and timber moulding together. Leave the bookcase down on the floor until the liquid nails has cured.
Once the glue is dry you can stand the bookcase up and put its shelves back in. Please remember to do a test fit first making sure that the panels at the back straighten out before putting any glue or stapling it together.
If you have any other questions we can help with, please let us know.