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We are given the following expression:

\[
\frac{(x + 1)}{2x(x - 1)}
\]

We need to identify an equivalent expression from the given options.

### Step 1: Simplify the given expression
The denominator can be factored:

\[
2x(x - 1) = 2x^2 - 2x
\]

So the original expression becomes:

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

### Step 2: Compare with the options
Let's now look at the options:

1. \(\frac{x + 1}{2x^2 - 2x}\)
2. \(\frac{1}{2x - 1}\)
3. \(\frac{1}{2x}\)
4. \(\frac{x + 1}{2x^2 - 1}\)

The first option matches exactly with our simplified form, which is:

\[
\frac{x + 1}{2x^2 - 2x}
\]

Thus, the correct answer is the first option.

---

Do you want further details or have any questions?

Here are 5 related questions for more practice:

1. How do you factor the expression \(2x^2 - 2x\)?
2. What steps can you take to simplify a rational expression?
3. Can this type of problem be solved using synthetic division?
4. What are common mistakes when simplifying expressions with polynomials?
5. How would you simplify \(\frac{x^2 - 1}{x - 1}\)?

**Tip:** Always check for factorable terms in both the numerator and the denominator when simplifying rational expressions!

Identifica la expresión equivalente a: (x + 1) / [2x(x - 1)]

Identify the expression equivalent to (x + 1) / [2x(x - 1)] by simplifying the denominator and comparing it to the provided options. Learn key algebraic concepts such as factoring and simplifying rational expressions. Suitable for students in Grades 8-10.

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