If limx→∞ x2+1x+1−ax−b=2, then

We have,limx→∞ x2+1x+1−ax−b=2⇒ limx→∞ x2(1−a)−x(a+b)+1−bx+1=2      …(i)Since the limit of the given expression is a finite non-zero number. Therefore, numerator and denominator are of the same degree. ∴ 1−a=0⇒a=1Putting a = 1 in (i), we obtainlimx→∞ −x(1+b)+(1−b)x+1=2⇒ −(1+b)=2⇒b=−3 Hence , a=1and b=-3