https://file.aiquickdraw.com/mathbot/file/17261350613236e831qpo.jpg

The problem asks you to simplify the following expression:

\[
\frac{1}{3(x + 1)} + 2
\]

Let's go through the steps:

### Step 1: Express 2 as a fraction
To add fractions, they need a common denominator. We can express the whole number 2 as a fraction with the same denominator:

\[
2 = \frac{2 \cdot 3(x + 1)}{3(x + 1)} = \frac{6(x + 1)}{3(x + 1)}
\]

### Step 2: Add the fractions
Now, the expression becomes:

\[
\frac{1}{3(x + 1)} + \frac{6(x + 1)}{3(x + 1)}
\]

Since the denominators are the same, we can add the numerators:

\[
\frac{1 + 6(x + 1)}{3(x + 1)}
\]

### Step 3: Simplify the numerator
Now simplify the numerator:

\[
1 + 6(x + 1) = 1 + 6x + 6 = 6x + 7
\]

So the final expression is:

\[
\frac{6x + 7}{3(x + 1)}
\]

Thus, the simplified form of the expression is:

\[
\frac{6x + 7}{3(x + 1)}
\]

Looking at the options provided in the image, this matches the first option:

\[
\frac{6x + 7}{3(x + 1)}
\]

Do you need further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you find a common denominator when adding fractions with different denominators?
2. What is the process for simplifying complex fractions?
3. Can you explain how to handle whole numbers when adding them to fractions?
4. What is the benefit of simplifying expressions before solving equations?
5. How do you determine if a fraction is in its simplest form?

### Tip:
Always ensure that denominators are identical when adding fractions; converting whole numbers into fractions is often helpful to avoid mistakes.

Write as a single fraction in its simplest form: 1/(3(x+1)) + 2

Learn how to simplify the expression 1/(3(x+1)) + 2 into a single fraction. This step-by-step guide explains how to express 2 as a fraction, find a common denominator, and add fractions. Perfect for Grades 7-9 students looking to improve their understanding of fractions and algebraic expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation