So many cracks

Let $u = \dfrac{2}{x - 2}$ $\Longrightarrow$ $f(u) = \dfrac{1}{(u - 6)(u - 11)}$

$f(u)$ is undefined when u is undefined i.e at $x = 2$ , $u = 6$ , $u = 11$ .

$\Longrightarrow$ $f(u)$ is discontinous at $x = 2$ , $\dfrac{2}{x - 2}= 6$ , $\dfrac{2}{x - 2} = 11$

i.e $x = 2$ , $x = \dfrac{7}{3}$ , $x = \dfrac{24}{11}$

Number of discontinuos points = $\boxed{3}$