Which Expression Is Equal To 3x/x+3+x/x+2? Let’s Break It Down, Step By Step!

Dr. Melissa Stoltenberg IV 24 May 2025

Math problems can sometimes feel like a maze, but don’t worry—this one’s got your back. If you’ve ever scratched your head over the question, “Which expression is equal to 3x/x+3+x/x+2?” well, you’re not alone. This algebraic puzzle is a common stumbling block for many students and even adults brushing up on their math skills. But guess what? By the end of this article, you’ll not only solve it but also understand the logic behind it. So, let’s dive in and unravel this mystery together!

Math might seem intimidating at first glance, but breaking it down into smaller pieces makes everything way easier. In this article, we’re going to focus on the expression “3x/x+3+x/x+2” and figure out exactly what it simplifies to. Whether you’re preparing for an exam or just want to sharpen your algebra skills, this guide will help you nail it.

We’ll walk through step-by-step explanations, throw in some useful tips, and even sprinkle a bit of humor along the way. Because let’s face it—math doesn’t have to be boring, right? So, buckle up and get ready to conquer this equation like a pro!

Here’s a quick roadmap of what we’ll cover:

Understanding the problem
Breaking down the expression
Simplifying step by step
Exploring common mistakes
Checking our work
Tips for mastering similar problems

Let’s get started!

Understanding the Problem: What Does This Expression Mean?

Before we jump into solving, let’s take a moment to understand what we’re dealing with here. The expression “3x/x+3+x/x+2” is essentially a combination of fractions and variables. At first glance, it might look complicated, but fear not—it’s actually quite manageable once you break it down.

Here’s the deal: The expression consists of two separate fractions added together. The first fraction is “3x/x+3,” and the second is “x/x+2.” Our goal is to simplify this entire expression into its most basic form. Sounds doable, right?

Breaking Down the Expression: Step by Step

Step 1: Identify the Fractions

First things first, let’s identify the individual fractions within the expression:

3x / (x + 3)
x / (x + 2)

Notice how both fractions have variables in their denominators. This is key because it means we’ll need to find a common denominator to combine them. But we’ll get to that in a bit. For now, just keep this in mind.

Step 2: Combine the Fractions

Now that we’ve identified the fractions, the next step is to combine them. To do this, we need to find the least common denominator (LCD). In this case, the LCD is (x + 3)(x + 2). Once we have that, we can rewrite both fractions with the same denominator.

Here’s what it looks like:

(3x(x + 2)) / ((x + 3)(x + 2))
(x(x + 3)) / ((x + 3)(x + 2))

Now that both fractions have the same denominator, we can combine them into a single fraction:

(3x(x + 2) + x(x + 3)) / ((x + 3)(x + 2))

Simplifying the Expression: The Magic Happens Here

Alright, now that we’ve combined the fractions, it’s time to simplify the numerator. Let’s expand the terms:

(3x^2 + 6x + x^2 + 3x) / ((x + 3)(x + 2))

Combine like terms:

(4x^2 + 9x) / ((x + 3)(x + 2))

And there you have it! The simplified expression is:

4x^2 + 9x / (x^2 + 5x + 6)

Common Mistakes to Avoid

When working with algebraic expressions, it’s easy to make mistakes. Here are a few common ones to watch out for:

Forgetting to find the least common denominator before combining fractions.
Not properly distributing terms when expanding.
Skipping steps or rushing through the process.

Remember, patience is key. Take your time and double-check each step to ensure accuracy.

Checking Your Work: Always Double-Verify

Once you’ve simplified the expression, it’s always a good idea to double-check your work. Here’s how you can do that:

Substitute a value for x (e.g., x = 1) and see if both the original and simplified expressions yield the same result.
Use a calculator or algebraic software to verify your calculations.

By verifying your work, you can ensure that your solution is correct and reliable.

Tips for Mastering Similar Problems

Tip 1: Practice Makes Perfect

The more you practice solving algebraic expressions, the better you’ll get. Start with simpler problems and gradually work your way up to more complex ones.

Tip 2: Break It Down

Whenever you encounter a complicated expression, break it down into smaller, manageable parts. This will make the problem seem less daunting and help you focus on one step at a time.

Tip 3: Stay Organized

Keep your work neat and organized. Write out each step clearly so you can easily follow your thought process and spot any mistakes.

Why Understanding Algebra Matters

Algebra isn’t just about solving equations—it’s a fundamental skill that applies to many areas of life. Whether you’re calculating budgets, analyzing data, or even just estimating tips at a restaurant, algebra plays a crucial role. By mastering expressions like “3x/x+3+x/x+2,” you’re building a strong foundation for future success.

Conclusion: You’ve Got This!

So, there you have it! The expression “3x/x+3+x/x+2” simplifies to:

4x^2 + 9x / (x^2 + 5x + 6)

By following the steps we’ve outlined, you’ve not only solved this problem but also gained valuable insights into how algebra works. Remember, math isn’t about memorizing formulas—it’s about understanding the logic behind them. Keep practicing, stay curious, and don’t be afraid to ask for help when you need it.

Now, here’s your call to action: Share this article with a friend who might find it helpful. Leave a comment below with your thoughts or any questions you have. And most importantly, keep exploring the world of math—it’s way more exciting than you might think!

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