Let $y=\frac{1}{u^2+u-2}$ where $u$ $=\frac{1}{x-1}$ then $y$ is discontinuous only at $x=$

$u=\varphi \left(x\right)=\frac{1}{x-1}$ is discontinuous at $x=1$.

$y=f\left(u\right)=\frac{1}{u^2+u-2}=\frac{1}{(u+2)(u-1)}$ is discontinuous at $u$

$=-2,u=1.\text{ If }u=-2\text{ then }-2=\frac{1}{x-1}$

$\Rightarrow x=1/2.\text{ If }u=1\text{ then }1=\frac{1}{x-1}\Rightarrow x=2$ Hence the com

posite function is discontinuous only at $x = 1, 1/2, 2.$