The given equation is:

\[
y = \frac{x}{(x-1)^2}
\]

Would you like me to perform a specific operation on this function, such as differentiation, integration, or analyzing critical points? Please specify.

Here are some possible related tasks:
1. Find the derivative of \( y \) with respect to \( x \).
2. Find the integral of \( y \) with respect to \( x \).
3. Identify any critical points (where the derivative is zero).
4. Analyze the asymptotic behavior of the function.
5. Solve for \( x \) when \( y = 0 \).

**Tip**: The function has a vertical asymptote at \( x = 1 \) due to the denominator \( (x-1)^2 \).

Explore the rational function y = x / (x-1)^2 with step-by-step solutions. Learn how to differentiate the function, find critical points, and analyze its asymptotic behavior. This problem is ideal for students in Grades 10-12 studying algebra and calculus.

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