What Is 2 + X 5 X − X − 2 5 X \frac{2+x}{5x} - \frac{x-2}{5x} 5 X 2 + X ​ − 5 X X − 2 ​ , For X ≠ 0 X \neq 0 X  = 0 , Expressed In Simplest Form?

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Introduction

When dealing with fractions, simplifying them is an essential step in solving mathematical problems. In this article, we will explore the process of simplifying a given expression involving fractions. The expression we will be working with is $\frac{2+x}{5x} - \frac{x-2}{5x}$, and we will find its simplest form for $x \neq 0$.

Understanding the Expression

The given expression is a difference of two fractions, both of which have the same denominator, which is $5x$. This means that we can combine the two fractions into a single fraction by subtracting their numerators. The expression can be rewritten as:

$$\frac{2+x}{5x} - \frac{x-2}{5x} = \frac{(2+x) - (x-2)}{5x}$$

Simplifying the Numerator

Now, let's simplify the numerator of the fraction. We can start by combining like terms:

$$(2+x) - (x-2) = 2 + x - x + 2$$

Combining Like Terms

When we combine like terms, we can add or subtract the coefficients of the same variables. In this case, we have:

$$2 + x - x + 2 = 2 + 2$$

Evaluating the Expression

Now, let's evaluate the expression by simplifying the numerator:

$$2 + 2 = 4$$

Writing the Simplified Expression

Now that we have simplified the numerator, we can write the simplified expression:

$$\frac{4}{5x}$$

Conclusion

In this article, we have simplified the given expression $\frac{2+x}{5x} - \frac{x-2}{5x}$ for $x \neq 0$. We started by rewriting the expression as a single fraction with a common denominator, and then simplified the numerator by combining like terms. Finally, we evaluated the expression and wrote the simplified form. The simplified expression is $\frac{4}{5x}$.

Final Answer

The final answer is $\boxed{\frac{4}{5x}}$.

Related Topics

• Simplifying fractions
• Combining like terms
• Evaluating expressions

Further Reading

• Simplifying Fractions
• Combining Like Terms
• Evaluating Expressions

References

• Math Is Fun
• Khan Academy
• Wikipedia

Tags

• Simplifying fractions
• Combining like terms
• Evaluating expressions
• Math
• Algebra
• Fractions
• Expressions

Categories

• Mathematics
• Algebra
• Fractions
• Expressions

Keywords

• Simplifying fractions
• Combining like terms
• Evaluating expressions
• Math
• Algebra
• Fractions
• Expressions

Meta Description

This article provides a step-by-step guide on simplifying the expression $\frac{2+x}{5x} - \frac{x-2}{5x}$ for $x \neq 0$. We will explore the process of simplifying fractions, combining like terms, and evaluating expressions. The final answer is $\boxed{\frac{4}{5x}}$.

Introduction

In our previous article, we explored the process of simplifying the expression $\frac{2+x}{5x} - \frac{x-2}{5x}$ for $x \neq 0$. We simplified the expression by combining like terms and evaluating the result. In this article, we will answer some frequently asked questions related to simplifying fractions and expressions.

Q&A

Q: What is the difference between simplifying fractions and simplifying expressions?

A: Simplifying fractions involves reducing a fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD). Simplifying expressions, on the other hand, involves combining like terms and eliminating any unnecessary operations.

Q: How do I simplify a fraction with a variable in the numerator or denominator?

A: To simplify a fraction with a variable in the numerator or denominator, you need to factor out the greatest common factor (GCF) of the numerator and denominator. For example, if you have the fraction $\frac{2x}{4x}$, you can simplify it by factoring out the GCF, which is $2x$.

Q: What is the order of operations when simplifying expressions?

A: The order of operations when simplifying expressions is:

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify a fraction with a negative exponent?

A: To simplify a fraction with a negative exponent, you need to rewrite the fraction with a positive exponent. For example, if you have the fraction $\frac{1}{x^{-2}}$, you can rewrite it as $x^2$.

Q: What is the difference between a like term and an unlike term?

A: A like term is a term that has the same variable and exponent, while an unlike term is a term that has a different variable or exponent. For example, $2x$ and $3x$ are like terms, while $2x$ and $3y$ are unlike terms.

Q: How do I simplify an expression with multiple like terms?

A: To simplify an expression with multiple like terms, you need to combine the coefficients of the like terms. For example, if you have the expression $2x + 3x + 4x$, you can combine the coefficients to get $9x$.

Conclusion

In this article, we have answered some frequently asked questions related to simplifying fractions and expressions. We have covered topics such as simplifying fractions with variables, the order of operations, simplifying fractions with negative exponents, and combining like terms. We hope that this article has provided you with a better understanding of how to simplify fractions and expressions.

Final Answer

The final answer is $\boxed{\frac{4}{5x}}$.

Related Topics

• Simplifying fractions
• Combining like terms
• Evaluating expressions
• Order of operations

Further Reading

• Simplifying Fractions
• Combining Like Terms
• Evaluating Expressions
• Order of Operations

References

• Math Is Fun
• Khan Academy
• Wikipedia

Tags

• Simplifying fractions
• Combining like terms
• Evaluating expressions
• Order of operations
• Math
• Algebra
• Fractions
• Expressions

Categories

• Mathematics
• Algebra
• Fractions
• Expressions

Keywords

• Simplifying fractions
• Combining like terms
• Evaluating expressions
• Order of operations
• Math
• Algebra
• Fractions
• Expressions

Meta Description

This article provides a Q&A guide on simplifying fractions and expressions. We cover topics such as simplifying fractions with variables, the order of operations, simplifying fractions with negative exponents, and combining like terms. The final answer is $\boxed{\frac{4}{5x}}$.