How does one work , 2x^2+x+3 divided by x-1

Question

anonymous · Answer

synthetic division or long division 
synthetic is easiest

anonymous · Answer

copy down the coefficients of $x^2+x+3$ 
    1     1    3

anonymous · Answer

then since you are dividing by $x-1$ put a $1$ on the side 

       1    1    3
1___________

anonymous · Answer

oops coefficients are 2,  1,  3 sorry
       2    1    3
1___________

anonymous · Answer

bring down the 2
       2    1    3
1___________
       2

anonymous · Answer

1 times 2 is 2
       2    1    3
1______2_____
       2

anonymous · Answer

add and get 
1 times 2 is 2
       2    1    3
1______2_____
       2     3

anonymous · Answer

1 times 3 is 3 

       2    1    3
1______2__3___
       2    3

anonymous · Answer

add and get 6
       2    1    3
1______2__3___
       2    3    6

anonymous · Answer

answer from the bottom row is $$2x+3+\frac{6}{x-1}$$

anonymous · Answer

thanks so much!