If limx→∞ x2+x+1x+1−ax−b=4 , then

We have, limx→∞ x2+x+1x+1−ax−b=4⇒ limx→∞ x2(1−a)+x(1−a−b)+1−bx+1=4lf  f(x) and g(x) are polynomials such that limx→∞ f(x)g(x) is a finite non-zero number, then f(x) and g(x) must be of the same degree. Therefore x2(1−a)+x(1−a−b)+1−b and x+1 must be of the same degree. This is possible only when a= 1. ln that case limx→∞ x2(1−a)+x(1−a−b)+1−bx+1=4⇒limx→∞ −xb+1−bx+1=4⇒−b=4⇒b=−4 Hence, a=1and  b=−4