Answer:
Option (2)
Step-by-step explanation:
Given expression is [tex]\frac{2}{(3x-1)}[/tex] ÷ [tex]\frac{6}{6x-1}[/tex]
We further simplify this expression,
[tex]\frac{2}{(3x-1)}[/tex] ÷ [tex]\frac{6}{6x-1}[/tex]
= [tex]\frac{2}{(3x-1)}\times \frac{6x-1}{6}[/tex]
= [tex]\frac{6x-1}{3(3x-1)}[/tex]
= [tex]\frac{6x-1}{(9x-3)}[/tex]
Therefore, [tex]\frac{6x-1}{(9x-3)}[/tex] will be the quotient of the given expression.
[tex]x\neq \frac{1}{3}[/tex] and [tex]x\neq \frac{1}{6}[/tex] for which the given expression is not defined.
Option (2) will be the answer.
