Changing y=x/(x+1) into a hyperbola?

Question

How do I put this: y=x/(x+1) into the form y=a/(x+b)+c? thankyou. workings shown would be appreciated!

Answer 1

y = x/(x + 1) = (x + 1 - 1)/(x + 1)

y = (x + 1)/(x + 1) - 1(x + 1) = 1 - 1/(x + 1)

y = -1/(x + 1) + 1