If $\;a+ib =\large\frac{(x+i)^{2}}{2x^{2}+1}\;$ , find $\;a^{2} +b^{2}$

Question

$(a)\;\large\frac{(x^{2}+1)^{2}}{(2x+1)^{2}}\qquad(b)\;\large\frac{(x+1)^{2}}{(2x+1)^{2}}\qquad(c)\;\large\frac{(x^{2}+1)^{2}}{(2x+1)}\qquad(d)\;\large\frac{(x^{2}+1)}{(2x+1)}$