Questions: Consider the following rational expression. 8y^3 - 27 / 2y - 3 Determine what value(s), if any, of the variable must be excluded.

Consider the following rational expression. 8y^3 - 27 / 2y - 3 Determine what value(s), if any, of the variable must be excluded.
Transcript text: Consider the following rational expression. \[ \frac{8 y^{3}-27}{2 y-3} \] Step 2 of 2: Determine what value(s), if any, of the variable must be excluded.
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Solution

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Solution Steps

Step 1: Identify the Denominator

The rational expression given is

\[ \frac{8 y^{3}-27}{2 y-3} \]

To determine the values that must be excluded from the domain, we focus on the denominator, which is

\[ 2y - 3 \]

Step 2: Set the Denominator to Zero

We need to find the value of \( y \) that makes the denominator equal to zero:

\[ 2y - 3 = 0 \]

Step 3: Solve for \( y \)

Solving the equation:

\[ 2y = 3 \implies y = \frac{3}{2} \]

Final Answer

The value that must be excluded from the domain is

\[ \boxed{y = \frac{3}{2}} \]

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