Solve for y in the equation 4y² / 2y = 6.

To solve the equation ( \frac{4y^2}{2y} = 6 ), start by simplifying the left side. The fraction ( \frac{4y^2}{2y} ) can be simplified by dividing both the numerator and denominator by ( 2y ), resulting in:

[

\frac{4y^2}{2y} = \frac{4}{2} \cdot \frac{y^2}{y} = 2y

]

Now, the equation simplifies to:

[

2y = 6

]

Next, divide both sides by 2 to isolate ( y ):

[

y = \frac{6}{2} = 3

]

Thus, the solution yields ( y = 3 ). This matches the provided answer.

This process highlights the importance of simplifying expressions correctly and performing arithmetic operations to isolate the variable. Understanding these steps is crucial in solving similar algebraic equations efficiently.