Given:
The expression is
[tex]\dfrac{12y^3-6y^2}{2y-1}[/tex], where [tex]y\neq \dfrac{1}{2}[/tex].
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{12y^3-6y^2}{2y-1}[/tex]
Taking out the common factors from the numerator, we get
[tex]\dfrac{12y^3-6y^2}{2y-1}=\dfrac{6y^2(2y-1)}{2y-1}[/tex]
Cancel out the common factors from numerator and denominator.
[tex]\dfrac{12y^3-6y^2}{2y-1}=6y^2[/tex]
Therefore, the simplified form of the given expression is [tex]6y^2[/tex].