The equation x2+x+12+1=x2+x+1x2−x−5 for x∈(−2,3) will have number of solutions,

x2+x+12+1=x2+x+1x2−x−5Since, x2+x+1>0∀x∈RDividing both sides by x2+x+1, we get            x2+x+1+1x2+x+1=x2−x−5∴  L.H.S. ≥2But x2−x−5<1 for x∈(−2,3)Therefore, the equation has no solution.