Find the Second Degree Taylor Polynomial Approximation Of $\frac{1}{1+x^{2}}$ About X = 1

Multiple Choice

Find the second degree Taylor polynomial approximation of $\frac{1}{1+x^{2}}$ about x = 1.

A) $\frac{1}{2}-\frac{x-1}{2}+\frac{(x-1) ^{2}}{4}$
B) $-\frac{1}{2}+\frac{x-1}{3}-\frac{(x-1) ^{2}}{4}$
C) $\frac{1}{2}-\frac{x-1}{4}+\frac{(x-1) ^{2}}{6}$
D) $-\frac{1}{2}+\frac{x-1}{3}-\frac{(x-1) ^{2}}{4}$ .