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

 

 $\mu =\varphi \left(x\right)=\frac{1}{x-1}$is discontinuous at $x=1$ ,
$y=f\left(\mu \right)=\frac{1}{{\mu }^1+\mu -2}=\frac{1}{\left(\mu +2\right)\left(\mu -1\right)}$ is discontinuous at  $\mu$
$=-2,\mu =1.$  If  $\mu =-2$ then  $-2=\frac{1}{x-1}$
$\Rightarrow x=1/2.$ If $\mu =1$ then $1=\frac{1}{x-1}\Rightarrow x=2.$  Hence the composite function is discontinuous only at  $x=1,1/2,2.$