To solve the equation

\[
\frac{t^2 + 2t + 1}{t + 1} = 4,
\]

we start by simplifying the expression on the left-hand side.

1. **Factor the numerator**: Notice that \( t^2 + 2t + 1 \) can be factored as \( (t + 1)^2 \). So, the equation becomes:

\[
\frac{(t + 1)^2}{t + 1} = 4.
\]

2. **Simplify the fraction**: Since \( t + 1 \) is a common factor in both the numerator and the denominator (assuming \( t \neq -1 \)), we can cancel it out:

\[
t + 1 = 4.
\]

3. **Solve for \( t \)**: Subtract 1 from both sides:

\[
t = 3.
\]

Thus, the solution is \( t = 3 \).

Would you like further details or explanations?

---

Here are five related questions to further explore the concepts:

1. How would the solution change if the equation were \( \frac{t^2 + 3t + 2}{t + 1} = 5 \)?
2. What is the impact on the solution if the denominator equals zero (e.g., \( t + 1 = 0 \))?
3. How can you verify that \( t = 3 \) is indeed the correct solution?
4. What are the implications of canceling terms in rational expressions?
5. How do you solve similar equations where the numerator isn't easily factorable?

**Tip:** Always check the domain of the variable in a rational expression to ensure that the denominator does not equal zero, as this would make the expression undefined.

Learn how to solve the rational equation (t^2 + 2t + 1)/(t + 1) = 4 with a detailed step-by-step solution. This problem covers algebraic concepts such as factoring quadratic expressions and solving rational equations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation