Simplify The Expression: $ 2m - \frac{1}{m}\$} Options A. { \frac{2m^2 - 1 {m}$}$ B. { \frac{1}{m}$}$ C. { \frac{2m - 1}{m}$}$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to solve problems more efficiently. It involves rewriting an expression in a simpler form, often by combining like terms or using algebraic properties. In this article, we will simplify the expression $2m - \frac{1}{m}$ and explore the different options available.

Understanding the Expression

The given expression is $2m - \frac{1}{m}$. This expression consists of two terms: $2m$ and $-\frac{1}{m}$. The first term is a simple variable term, while the second term is a fraction with a negative sign.

Option A: $\frac{2m^2 - 1}{m}$

One possible option for simplifying the expression is to combine the two terms into a single fraction. To do this, we need to find a common denominator for both terms. In this case, the common denominator is $m$. We can rewrite the expression as follows:

$$2m - \frac{1}{m} = \frac{2m^2}{m} - \frac{1}{m} = \frac{2m^2 - 1}{m}$$

This option is a valid simplification of the original expression.

Option B: $\frac{1}{m}$

Another possible option for simplifying the expression is to ignore the $2m$ term and only consider the fraction $-\frac{1}{m}$. However, this option is not a valid simplification of the original expression, as it does not take into account the $2m$ term.

Option C: $\frac{2m - 1}{m}$

A third possible option for simplifying the expression is to combine the two terms into a single fraction, but without the $m^2$ term. To do this, we can rewrite the expression as follows:

$$2m - \frac{1}{m} = \frac{2m^2}{m} - \frac{1}{m} = \frac{2m^2 - 1}{m} = \frac{2m - 1}{m}$$

However, this option is not a valid simplification of the original expression, as it does not take into account the $m^2$ term.

Conclusion

In conclusion, the correct simplification of the expression $2m - \frac{1}{m}$ is $\frac{2m^2 - 1}{m}$. This option takes into account both the $2m$ term and the fraction $-\frac{1}{m}$, and is a valid simplification of the original expression.

Why is Option A the Correct Answer?

Option A is the correct answer because it takes into account both the $2m$ term and the fraction $-\frac{1}{m}$. The $2m$ term can be rewritten as $\frac{2m^2}{m}$, and when we subtract the fraction $-\frac{1}{m}$, we get $\frac{2m^2 - 1}{m}$. This option is a valid simplification of the original expression, and is the only option that takes into account both terms.

Why are Options B and C Incorrect?

Options B and C are incorrect because they do not take into account both terms of the original expression. Option B ignores the $2m$ term, while Option C ignores the $m^2$ term. Both options are incomplete and do not provide a valid simplification of the original expression.

Tips and Tricks

When simplifying expressions, it's essential to take into account all the terms involved. In this case, we need to consider both the $2m$ term and the fraction $-\frac{1}{m}$. By combining these terms into a single fraction, we can simplify the expression and arrive at the correct answer.

Common Mistakes

When simplifying expressions, it's easy to make mistakes. Some common mistakes include:

• Ignoring one or more terms
• Not finding a common denominator
• Not simplifying the expression correctly

To avoid these mistakes, it's essential to carefully read and understand the expression, and to take your time when simplifying it.

Conclusion

Introduction

In our previous article, we simplified the expression $2m - \frac{1}{m}$ and arrived at the correct answer: $\frac{2m^2 - 1}{m}$. However, we know that there are many more questions and doubts that our readers may have. In this article, we will address some of the most frequently asked questions and provide additional information to help you better understand the concept.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same. In the expression $2m - \frac{1}{m}$, $m$ is a variable, while $2$ and $1$ are constants.

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

A: To simplify an expression with multiple terms, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, in the expression $2m + 3m$, the like terms are $2m$ and $3m$. You can combine these terms by adding their coefficients: $2m + 3m = 5m$.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a part of a whole using a decimal point. For example, the fraction $\frac{1}{2}$ is equal to the decimal $0.5$.

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, you need to find a common denominator for all the fractions in the expression. Then, you can combine the fractions by adding or subtracting their numerators. For example, in the expression $\frac{1}{2} + \frac{1}{3}$, the common denominator is $6$. You can rewrite the fractions as follows: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

Q: What is the difference between a positive and negative exponent?

A: A positive exponent indicates that the variable is raised to a power, while a negative exponent indicates that the variable is raised to a power and then taken to the reciprocal. For example, in the expression $x^2$, the exponent is positive. However, in the expression $\frac{1}{x^2}$, the exponent is negative.

Q: How do I simplify an expression with a negative exponent?

A: To simplify an expression with a negative exponent, you need to take the reciprocal of the variable and change the sign of the exponent. For example, in the expression $\frac{1}{x^2}$, you can rewrite it as $x^{-2}$.

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is an expression that can be expressed as a ratio of two integers, while an irrational expression is an expression that cannot be expressed as a ratio of two integers. For example, the rational expression $\frac{1}{2}$ can be expressed as a ratio of two integers, while the irrational expression $\sqrt{2}$ cannot be expressed as a ratio of two integers.

Q: How do I simplify an expression with a rational and an irrational term?

A: To simplify an expression with a rational and an irrational term, you need to separate the terms and simplify each term separately. For example, in the expression $\frac{1}{2} + \sqrt{2}$, you can separate the terms and simplify each term separately: $\frac{1}{2} + \sqrt{2} = \frac{1}{2} + \sqrt{2}$.

Conclusion

In conclusion, simplifying expressions is an essential skill that helps us to solve problems more efficiently. By understanding the concepts of variables, constants, fractions, decimals, exponents, and rational and irrational expressions, you can simplify expressions like $2m - \frac{1}{m}$ and arrive at the correct answer. We hope that this Q&A article has helped you to better understand the concept and has provided you with the tools and techniques you need to simplify expressions like this one.