(2b^+2b-6)/(b-2)

Hint:

factorize the numerator:
2b²+2b-6
=2(b²+b-3)
which does not have rational factors.

You will need to do a division, which is called the Euclidean division (long division), or another method is the synthetic division.

It is a little difficult to show the method here because it is almost impossible to line up numbers in the long division. The first reference below gives a good example of how to do long divisions.

Some references:

http://www.math.utah.edu/online/1010/euclid/

http://www.youtube.com/watch?v=4xANqGj7nnI