What Is The Value Of The Rational Expression Below When $x$ Is Equal To $6$?$\frac{x-2}{x-5}$A. 4 B. 3 C. $\frac{2}{5}$ D. 8

Introduction to Rational Expressions

Rational expressions are a type of algebraic expression that involves fractions with variables in the numerator and/or denominator. They are an essential concept in mathematics, particularly in algebra and calculus. In this article, we will focus on finding the value of a rational expression when a variable is equal to a specific value.

Understanding the Given Rational Expression

The given rational expression is $\frac{x-2}{x-5}$. To find its value when $x$ is equal to $6$, we need to substitute $x$ with $6$ in the expression.

Substituting x with 6 in the Rational Expression

To substitute $x$ with $6$ in the rational expression, we replace every instance of $x$ with $6$. This gives us:

$$\frac{6-2}{6-5}$$

Simplifying the Expression

Now, we simplify the expression by performing the arithmetic operations in the numerator and denominator.

$$\frac{6-2}{6-5} = \frac{4}{1}$$

Evaluating the Expression

The simplified expression is $\frac{4}{1}$, which is equal to $4$. Therefore, the value of the rational expression when $x$ is equal to $6$ is $4$.

Conclusion

In this article, we have discussed how to find the value of a rational expression when a variable is equal to a specific value. We have used the given rational expression $\frac{x-2}{x-5}$ and substituted $x$ with $6$ to find its value. The result is $4$, which is the correct answer.

Frequently Asked Questions

• What is a rational expression?
• How do you simplify a rational expression?
• What is the value of the rational expression when $x$ is equal to $6$?

Answer to Frequently Asked Questions

• A rational expression is a type of algebraic expression that involves fractions with variables in the numerator and/or denominator.
• To simplify a rational expression, you need to perform the arithmetic operations in the numerator and denominator.
• The value of the rational expression when $x$ is equal to $6$ is $4$.

Step-by-Step Solution

1. Substitute $x$ with $6$ in the rational expression.
2. Simplify the expression by performing the arithmetic operations in the numerator and denominator.
3. Evaluate the expression to find its value.

Common Mistakes to Avoid

• Not substituting $x$ with the correct value.
• Not simplifying the expression correctly.
• Not evaluating the expression to find its value.

Real-World Applications

Rational expressions have many real-world applications, such as:

• Calculating the area and perimeter of shapes.
• Finding the volume of solids.
• Solving problems in physics and engineering.

Final Thoughts

In conclusion, finding the value of a rational expression when a variable is equal to a specific value is an essential concept in mathematics. By following the steps outlined in this article, you can easily find the value of a rational expression and apply it to real-world problems.

Introduction

In our previous article, we discussed how to find the value of a rational expression when a variable is equal to a specific value. In this article, we will provide a Q&A section to help you better understand the concept and address any questions you may have.

Q&A Section

Q: What is a rational expression?

A: A rational expression is a type of algebraic expression that involves fractions with variables in the numerator and/or denominator.

Q: How do you simplify a rational expression?

A: To simplify a rational expression, you need to perform the arithmetic operations in the numerator and denominator. This may involve factoring, canceling out common factors, or combining like terms.

Q: What is the value of the rational expression when x is equal to 6?

A: The value of the rational expression when x is equal to 6 is 4. This is found by substituting x with 6 in the expression and simplifying.

Q: Can you provide an example of a rational expression?

A: Yes, here is an example of a rational expression: $\frac{x+3}{x-2}$. This expression involves a variable (x) in the numerator and denominator.

Q: How do you handle fractions with variables in the numerator and/or denominator?

A: To handle fractions with variables in the numerator and/or denominator, you need to follow the order of operations (PEMDAS) and perform the arithmetic operations in the numerator and denominator.

Q: Can you provide a step-by-step solution to finding the value of a rational expression?

A: Yes, here is a step-by-step solution to finding the value of a rational expression:

1. Substitute the variable with the given value.
2. Simplify the expression by performing the arithmetic operations in the numerator and denominator.
3. Evaluate the expression to find its value.

Q: What are some common mistakes to avoid when finding the value of a rational expression?

A: Some common mistakes to avoid when finding the value of a rational expression include:

• Not substituting the variable with the correct value.
• Not simplifying the expression correctly.
• Not evaluating the expression to find its value.

Q: What are some real-world applications of rational expressions?

A: Rational expressions have many real-world applications, such as:

• Calculating the area and perimeter of shapes.
• Finding the volume of solids.
• Solving problems in physics and engineering.

Q: Can you provide a final thought on rational expressions?

A: In conclusion, rational expressions are an essential concept in mathematics, and finding their value is a crucial skill to master. By following the steps outlined in this article and avoiding common mistakes, you can easily find the value of a rational expression and apply it to real-world problems.

Additional Resources

• For more information on rational expressions, visit the Khan Academy website.
• For practice problems and exercises, visit the Mathway website.
• For a comprehensive guide to algebra, visit the Algebra.com website.

Conclusion

In this article, we have provided a Q&A section to help you better understand the concept of rational expressions and find their value. We have also provided a step-by-step solution, common mistakes to avoid, and real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can easily find the value of a rational expression and apply it to real-world problems.