Question

For what value(s) of the variable is the expression undefined?
d-2/3d^2-10d+8

Answer 1

When it is undefined, the denominator =0
So, put 3d^2-10d+8 =0
(3d-4)(d-2)=0
(3d-4)=0 or (d-2)=0
d = 4/3 or d=2
So, when d =4/3 or d =2 , the expression is undefined~

Answer 2

Note that anything divided by 0 is undefined :|

Answer 3

factorise the denominator

\[\frac{d -2}{(3d - 4)(d -2)}\]

this simplifies to

\[\frac{1}{3d - 4}\]

there are a couple of things in the problem

there restrictions on the domain are all real x except x cannot equal 2 or 4/3

x = 4/3 will be a vertical asymptote

and

x = 2 is a point of discontinuity