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Let's simplify the given expression by removing factors of 1.

The expression is:

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

### Step 1: Factor both the numerator and the denominator.

- **Numerator**: \( t^2 - 1 \) is a difference of squares and can be factored as:
  \[
  t^2 - 1 = (t - 1)(t + 1)
  \]

- **Denominator**: \( t^2 - 2t + 1 \) is a perfect square trinomial and can be factored as:
  \[
  t^2 - 2t + 1 = (t - 1)^2
  \]

### Step 2: Rewrite the expression using these factors:

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

### Step 3: Simplify by canceling out common factors.

You can cancel one \( (t - 1) \) term from the numerator and denominator:

\[
\frac{t + 1}{t - 1}
\]

So, the simplified expression is:

\[
\frac{t + 1}{t - 1}
\]

Would you like more details or have any questions?

### Relative Questions:
1. How can the difference of squares be recognized in polynomial expressions?
2. What other methods can be used to factor trinomials besides the perfect square method?
3. How does the simplification process change if there are no common factors to cancel?
4. Can you simplify the expression \( \frac{t^2 + 2t + 1}{t^2 - 4} \)?
5. What is the next step if an expression cannot be factored easily?

### Tip:
When simplifying fractions, always check for common factors in the numerator and denominator that can be canceled out to simplify the expression.

Simplify by removing factors of 1: (t^2 - 1) / (t^2 - 2t + 1)

Simplify the algebraic expression (t^2 - 1) / (t^2 - 2t + 1) by removing factors of 1. This problem involves factoring a difference of squares and a perfect square trinomial, suitable for students in Grades 9-10.

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