Express (6x^(2)+x+2)/(2x^(2)-x+1) in the form P+(Qx+R)/(2x^(2)-x+1)?

Divide (6x^(2)+x+2) by (2x^(2)-x+1)

You should get a quotient 3 and remainder 5x-1

so it is 3+ (5x-1) / (2x^(2)-x+1)

Because the degree of nominator is bigger than the denominator so you have to do a long division.
Note: practice long division