已知 a,b∈R,a+b=4a,b \in \mathrm{R},a + b = 4a,b∈R,a+b=4 ,则 1a2+1+1b2+1\frac{1}{{a}^{2} + 1} + \frac{1}{{b}^{2} + 1}a2+11+b2+11 的最大值为（ ）A. 5+12\frac{\sqrt{5} + 1}{2}25+1B. 5+22\frac{\sqrt{5} + 2}{2}25+2C. 5+14\frac{\sqrt{5} + 1}{4}45+1D. 5+24\frac{\sqrt{5} + 2}{4}45+2