You cannot serve two masters...You cannot serve God and anxiety/worries. Why is it impossible to serve two masters? Isn’t it somehow plausible to be at the service of two or even three masters, as long as each is allotted his own time? Jesus was speaking from experience. He must have seen how men and women exhaust themselves with anxiety and worries in their attempt to please more than one master. But Jesus was not speaking about human masters. He was talking about the one and only master, God. 
Serving two masters is indeed impossible to pull off, especially when it comes to serving God,  for our Lord is a jealous God. Service demands total attention and doesn't allow for distractions.  Anxiety and/or worries are distractive, and they become great obstacles in one's ability to offer a service. Serving God is very much unlike serving as we know it. Serving God isn't so much an action as it is inaction. Serving God requires that we just  be, that we surrender ourselves to God's will and allow God to direct and guide our ways. Serving God requires that we let go of everything upon which we cling in order to  bewho/what we were meant to be: sons and daughters of God. Anxiety and/or worries can prevent us from realizing this, for the moment we start being anxious about our tomorrows, we begin disengaging ourselves from God's grip. When we are worrisome about what we will eat and wear, we tell God that God can't take care of us, that we have to take leave of God so that we can take care of our tomorrows. Says Jesus: “ Remain at the feet of God and serve God. Just be there. Let God serve you. Let God take care of you. Serve God by letting God serve you. Just be.”