To solve the equation:

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

we can start by simplifying the left-hand side. Notice that the numerator \( t^2 + 2t + 1 \) is a perfect square trinomial:

\[
t^2 + 2t + 1 = (t + 1)^2.
\]

So the equation becomes:

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

We can simplify further by canceling out \( t + 1 \) from the numerator and denominator:

\[
t + 1 = 4.
\]

Now, solve for \( t \) by subtracting 1 from both sides:

\[
t = 3.
\]

So the solution is:

\[
\boxed{t = 3}.
\]

Would you like more details or have any questions? Here are some related questions for practice:

1. What happens if \( t + 1 = 0 \) in the original equation?
2. How would you solve the equation if it was \( \frac{t^2 + 2t + 1}{t + 1} = 5 \) instead?
3. What is the value of \( t \) if the equation was \( \frac{t^2 - 4t + 4}{t - 2} = 2 \)?
4. How do you factor \( t^2 + 2t + 1 \) directly?
5. What if the equation had been \( \frac{t^2 + 4t + 4}{t + 2} = 4 \)?

**Tip:** Always check if the numerator can be factored to simplify the equation before solving it.

Learn how to solve the equation (t^2 + 2t + 1) / (t + 1) = 4 step-by-step with detailed explanations. This problem involves simplifying rational expressions and solving quadratic equations, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation