Should you workout with an injury?

As a personal trainer, every day I work with different people that meet obstacles when it's to make it to the gym. Sometimes it's lack of motivation, busy work schedule, or personal commitments. But health should be a priority for all of us and instead finding excuses for living a sedentary life we should find ways to get motivated.
One of the excuses people use is that they have an injury and they don't want to make things worse. It's true that doing exercises with an improper technique, we can get injured or we can make a injury even worse. But if you get medical advice, you'll know what you should avoid, and what is recommended for you to do when you are exercising. If somebody has a shoulder injury for example, it's OK to train the legs and do core exercises.
On the other hand, inactivity makes your body weaker, which could potentially prolong your injury. Physiotherapists can often recommend great exercises as well as what to avoid. And let's remember that exercise is a great mood enhancer and a good stress reliever. By exercising we improve the body, the mind and the soul.