Compatibility issue when using android app in both phone and tablet and image using background of some views then image get stretched fit the screen size and some time resolution also lost and will not work good in bigger screen.
3 Answers
Compatibility issue generally arises when our application is downloaded in to device with different screen size and resolution so first basic problem happen in tablet activity not use space efficient so we have to use fragment also. and the second problem may come in image scaling and re sizing so we have to use 9patch tool and third problem may come if we use hard coded and absolute pixel in xml layout file so please avoid it.
First, take a look at this
For managing images i use to do the following:
-Put your highest resolution of the image at the -nodpi folder
-Use code to scale it so that the image width matches the screen width
-Put it at the imageview and use ScaleType.Matrix but dont set a matrix
Your image will fit perfectly, but, you still need to take care of the aspect ratio.
My approach is to desing images at 16/9 and let know the designer that the bottom of the image (usually between <1.5,1.7>) will not be shown on devices with less aspect ratio so he will not put relevant design elements on it.
Hope this helps.
Please read these Documents and apply :-
http://developer.android.com/guide/practices/screens_support.html
http://developer.android.com/training/multiscreen/screensizes.html

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