Answer-
The interval where the function is diffrentiable is
[tex][-\infty,1)\ \bigcup\ (1,\infty][/tex]
Solution-
The given expression is,
[tex]y=\dfrac{3}{2(x-1)}[/tex]
The function will be differentiable where it is continuous and it will not be differentiable, where the function is not continuous.
The function continuous everywhere except at x = 1, because
[tex]\Rightarrow 2(x-1)=0\\\\\Rightarrow x-1=0\\\\\Rightarrow x=1[/tex]
at x = 1, its limit does not exist.
Therefore, apart from x=1, this function is differentiable everywhere. The interval will be
[tex][-\infty,1)\ \bigcup\ (1,\infty][/tex]
