limx→∞ x2+x+1−x2+1=

Here, the expression assumes the form ∞ - ∞asx→∞.So, we reduce it to the rational form f(x)g(x)We have,limx→∞ x2+x+1−x2+1=limx→∞ x2+x+1−x2+1x2+x+1+x2+1x2+x+1+x2+1=limx→∞ x2+x+1−x2−1x2+x+1+x2+1=limx→∞ xx2+x+1+x2+1=limx→∞ 11+1x+1x2+1+1x2               [Dividing N, and D' by x]=11+1=12