\(\frac{\left(x^2+a\right)\left(1+a\right)a^2x^2+1}{\left(x^2-a\right)\left(1-a\right)+a^2x^2+1}=\frac{x^2+x^2a+a+a^2+a^2x^2+1}{x^2-x^2a-a+a^2+a^2x^2+1}\)\(=\frac{x^2+x^2a+a^2x^2+1+a+a^2}{x^2-x^2a+a^2x^2+1-a+a^2}=\frac{x^2\left(1+a+a^2\right)+\left(1+a+a^2\right)}{x^2\left(1-a+a^2\right)+\left(1-a+a^2\right)}\)
\(=\frac{\left(x^2+1\right)\left(1+a+a^2\right)}{\left(x^2+1\right)\left(1-a+a^2\right)}=\frac{1+a+a^2}{1-a+a^2}\)