Simplify. Express Your Answer As A Single Fraction In Simplest Form.${ \frac{2}{t+4} + \frac{2}{t+4} }$

Introduction

In mathematics, simplifying algebraic expressions is a crucial skill that helps us to solve equations and inequalities more efficiently. When we add or subtract fractions, we need to find a common denominator to combine them. In this article, we will focus on simplifying the expression $\frac{2}{t+4} + \frac{2}{t+4}$ and provide a step-by-step guide on how to simplify algebraic expressions.

Understanding the Problem

The given expression is $\frac{2}{t+4} + \frac{2}{t+4}$. We can see that both fractions have the same denominator, which is $t+4$. To simplify this expression, we need to find a common denominator and combine the fractions.

Step 1: Find a Common Denominator

Since both fractions have the same denominator, we can simply add the numerators together. The common denominator is $t+4$, so we can write the expression as:

$$\frac{2}{t+4} + \frac{2}{t+4} = \frac{2+2}{t+4}$$

Step 2: Simplify the Numerator

Now that we have added the numerators, we can simplify the expression by combining the like terms. In this case, we have $2+2$, which equals $4$. So, the expression becomes:

$$\frac{2+2}{t+4} = \frac{4}{t+4}$$

Step 3: Simplify the Fraction

The fraction $\frac{4}{t+4}$ is already in its simplest form, as the numerator and denominator have no common factors. Therefore, the final simplified expression is:

$$\frac{4}{t+4}$$

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics that helps us to solve equations and inequalities more efficiently. By following the steps outlined in this article, we can simplify expressions like $\frac{2}{t+4} + \frac{2}{t+4}$ and arrive at the final answer. Remember to always find a common denominator, simplify the numerator, and simplify the fraction to arrive at the final answer.

Tips and Tricks

• When adding or subtracting fractions, always find a common denominator.
• Simplify the numerator by combining like terms.
• Simplify the fraction by dividing both the numerator and denominator by their greatest common factor.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, we use algebraic expressions to describe the motion of objects, while in engineering, we use them to design and optimize systems. In economics, we use algebraic expressions to model economic systems and make predictions about future trends.

Common Mistakes to Avoid

• Failing to find a common denominator when adding or subtracting fractions.
• Not simplifying the numerator by combining like terms.
• Not simplifying the fraction by dividing both the numerator and denominator by their greatest common factor.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill that helps us to solve equations and inequalities more efficiently. By following the steps outlined in this article, we can simplify expressions like $\frac{2}{t+4} + \frac{2}{t+4}$ and arrive at the final answer. Remember to always find a common denominator, simplify the numerator, and simplify the fraction to arrive at the final answer.

Final Answer

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Introduction

In our previous article, we discussed the importance of simplifying algebraic expressions and provided a step-by-step guide on how to simplify expressions like $\frac{2}{t+4} + \frac{2}{t+4}$. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What is the purpose of simplifying algebraic expressions?

A: The purpose of simplifying algebraic expressions is to make them easier to work with and to arrive at the final answer more efficiently. Simplifying expressions helps us to:

• Solve equations and inequalities more efficiently
• Understand complex concepts more easily
• Make predictions about future trends in fields such as physics, engineering, and economics

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Find a common denominator when adding or subtracting fractions.
2. Simplify the numerator by combining like terms.
3. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor.

Q: What is a common denominator?

A: A common denominator is a number that both fractions can be divided by. When adding or subtracting fractions, we need to find a common denominator to combine them.

Q: How do I find a common denominator?

A: To find a common denominator, look for the least common multiple (LCM) of the denominators. For example, if we have two fractions with denominators 4 and 6, the LCM is 12. Therefore, the common denominator is 12.

Q: What is the difference between simplifying and solving an equation?

A: Simplifying an equation involves reducing the equation to its simplest form, while solving an equation involves finding the value of the variable that makes the equation true.

Q: Can I simplify an expression with variables in the denominator?

A: Yes, you can simplify an expression with variables in the denominator. However, you need to be careful when simplifying expressions with variables in the denominator, as the variable may be a factor of the denominator.

Q: How do I simplify an expression with a variable in the denominator and a fraction in the numerator?

A: To simplify an expression with a variable in the denominator and a fraction in the numerator, follow these steps:

1. Simplify the fraction in the numerator.
2. Simplify the expression by dividing both the numerator and denominator by their greatest common factor.

Q: Can I simplify an expression with a negative exponent?

A: Yes, you can simplify an expression with a negative exponent. To simplify an expression with a negative exponent, follow these steps:

1. Rewrite the expression with a positive exponent.
2. Simplify the expression by dividing both the numerator and denominator by their greatest common factor.

Q: How do I simplify an expression with a radical in the denominator?

A: To simplify an expression with a radical in the denominator, follow these steps:

1. Simplify the radical in the denominator.
2. Simplify the expression by dividing both the numerator and denominator by their greatest common factor.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill that helps us to solve equations and inequalities more efficiently. By following the steps outlined in this article, we can simplify expressions like $\frac{2}{t+4} + \frac{2}{t+4}$ and arrive at the final answer. Remember to always find a common denominator, simplify the numerator, and simplify the fraction to arrive at the final answer.

Final Answer

The final answer is $\boxed{\frac{4}{t+4}}$.