Solution x2+1(x+1)(x−1)\frac{x^2+1}{(x+1)(x-1)}(x+1)(x−1)x2+1 First make it a mixed form: x2+1x2−1=1+2x2−1\frac{x^2+1}{x^2-1}=1+\frac{2}{x^2-1}x2−1x2+1=1+x2−12 Now: 2x2−1=1x−1−1x+1\frac{2}{x^2-1}=\frac{1}{x-1}-\frac{1}{x+1}x2−12=x−11−x+11 Hence: x2+1(x+1)(x−1)=1+1x−1−1x+1\boxed{\frac{x^2+1}{(x+1)(x-1)}=1+\frac{1}{x-1}-\frac{1}{x+1}}(x+1)(x−1)x2+1=1+x−11−x+11