2. Solve the equation $\left(1-\left(1+x^{-2}\right)^{-1}\right)^{-1}=3.25$.


2. We organize the inner parenthesis $\left(1-\left(1+\frac{1}{x^{2}}\right)^{-1}\right)^{-1}=3.25$, expand to a common denominator $\left(1-\left(\frac{x^{2}+1}{x^{2}}\right)^{-1}\right)^{-1}=3.25$. We consider the negative exponent $\left(1-\frac{x^{2}}{x^{2}+1}\right)^{-1}=3.25$ and expand again to a common denominator $\left(\frac{x^{2}+1-x^{2}}{x^{2}+1}\right)^{-1}=3.25$. We consider the negative exponent again $\frac{x^{2}+1}{1}=3.25$, simplify $x^{2}=2.25$ and take the square root. We calculate the solutions $x_{1}=1.5$ and $x_{2}=-1.5$.
Considering the negative exponent $1+\frac{1}{x^{2}}$ ..... 1 point
Expanding to a common denominator $\frac{x^{2}+1}{x^{2}}$ ..... 1 point
Considering the negative exponent $1-\frac{x^{2}}{x^{2}+1}$ ..... 1 point
Expanding to a common denominator $\frac{x^{2}+1-x^{2}}{x^{2}+1} \ldots$ ..... 1 point
Simplifying the equation $x^{2}=2.25$ ..... 1 point
Calculated solutions $x_{1}=1.5$ and $x_{2}=-1.5$ ..... 1 point