When the degree of the numerator is exactly one more than the degree of the denominator, the graph of the rational function will have an oblique asymptote.

To find the equation of the oblique asymptote, perform long division (synthetic if it will work) by dividing the denominator into the numerator.  So, to find the equation of the oblique asymptote, perform the long division and discard the remainder.

let us assume denominator of function is ax+b and  after performing long division we found remainder c

since equation of oblique assymtote is y=2x+1

therefore numerator of function = (2x+1)(ax+b)+c(remainder)

                                             =2ax2+(a+2b)x+b+c

therefore rational function f(x) =[2ax2+(a+2b)x+b+c] / (ax+b