Chapter 11 - Quadratic Functions and Equations - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 714: 61

$$x=1,\:x=-2$$

To find the x-intercepts, we set the function equal to zero. Doing this, we find: $$ 0=\frac{x^2}{x-2}+1\\ -1=\frac{x^2}{x-2}\\ -\left(x-2\right)=x^2\\ x^2+x-2=0\\ x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-2\right)}}{2\cdot \:1}\\ x=1,\:x=-2$$