The value of the constants α and β such that limx→∞ x2+1x+1−αx−β=0 are , respectively

Given,limx→∞ x2+1x+1−αx−β=0⇒limx→∞ x2+1−αx2+x−β(x+1)x+1=0⇒ limx→∞ 2x−α(2x+1)−β(1)1=0[using L' Hospital's rule] lf this limit is zero, then the function 2x−α(2x+1)−β=0⇒ x(2−2α)−(α+β)=0Equating the coefficient of x and constant terms, we get2−2α=0and   α+β=0⇒α=1,β=−1