What is this type of division called and how do you do it?

\({5x-2\over x+3} = 5 - {17 \over x+3}~\\ \qquad 5(x+3)=5x+15\\ LHS\\={5x-2\over x+3}\\={5(x+3)-15-2\over x+3}\\={5(x+3)-17\over x+3}\\= {5(x+3)\over x+3}-{17\over x+3}\\= 5-{17\over x+3}\ \)

 

This is not really what you were expected to do though.

You were expected to do algebraic division or synthetic division

 

This is an example of what you were supposed to do :)

 

https://www.youtube.com/watch?v=H94ma2ofGuc