The given equation is:

\[
\frac{8}{x(2x)} = y
\]

Let's simplify the expression step-by-step:

1. Multiply \( x \) and \( 2x \) in the denominator:
\[
x(2x) = 2x^2
\]

Now, the equation becomes:
\[
\frac{8}{2x^2} = y
\]

2. Simplify the fraction:
\[
\frac{8}{2x^2} = \frac{4}{x^2}
\]

So, the simplified equation is:
\[
\frac{4}{x^2} = y
\]

Would you like further details on how to manipulate or solve this equation? Here are a few related questions to consider:

1. What is the value of \( x \) when \( y \) is given?
2. How do you solve for \( x \) if \( y \) is known?
3. How does the equation change if the numerator changes from 8 to another value?
4. What is the behavior of \( y \) as \( x \) approaches 0?
5. Can you plot the graph of \( y = \frac{4}{x^2} \)?

**Tip:** Always simplify expressions before solving for variables to make the process clearer!

Learn how to simplify the rational expression 8 / x(2x) = y with a detailed step-by-step solution. This problem focuses on algebraic simplification and rational expressions, making it ideal for students in Grades 8-10.

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