Certainly! Here is the transcription of the image written for an educational website: --- ### Algebraic Expression Simplification Consider the following algebraic expression that needs to be simplified: \[ \frac{6x^2 + 17x - 40}{x^2 + x - 20} + \frac{3}{x - 4} - \frac{5x}{x + 5} \] Let's break down and simplify this expression step by step. 1. **Identify Common Factors:** - Factorize the quadratic expressions in the denominators, if possible. - Determine a common denominator that can simplify the addition and subtraction of these rational expressions. 2. **Simplify Each Term:** - Simplify the individual fractions before attempting to combine them. 3. **Combine the Fractions:** - Once simplified, use the common denominator to combine the terms into a single rational expression. 4. **Check for Any Further Simplifications:** - After combining, verify if the resulting expression can be further simplified by canceling common factors in the numerator and denominator. By following these steps, you can effectively simplify complex algebraic expressions. Let’s apply this to the given expression and work through the solution. --- This transcription outlines the algebraic expression and sets the stage for a step-by-step simplification process, which would be useful for educational purposes.
Certainly! Here is the transcription of the image written for an educational website: --- ### Algebraic Expression Simplification Consider the following algebraic expression that needs to be simplified: \[ \frac{6x^2 + 17x - 40}{x^2 + x - 20} + \frac{3}{x - 4} - \frac{5x}{x + 5} \] Let's break down and simplify this expression step by step. 1. **Identify Common Factors:** - Factorize the quadratic expressions in the denominators, if possible. - Determine a common denominator that can simplify the addition and subtraction of these rational expressions. 2. **Simplify Each Term:** - Simplify the individual fractions before attempting to combine them. 3. **Combine the Fractions:** - Once simplified, use the common denominator to combine the terms into a single rational expression. 4. **Check for Any Further Simplifications:** - After combining, verify if the resulting expression can be further simplified by canceling common factors in the numerator and denominator. By following these steps, you can effectively simplify complex algebraic expressions. Let’s apply this to the given expression and work through the solution. --- This transcription outlines the algebraic expression and sets the stage for a step-by-step simplification process, which would be useful for educational purposes.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Perform the operation
![Certainly! Here is the transcription of the image written for an educational website:
---
### Algebraic Expression Simplification
Consider the following algebraic expression that needs to be simplified:
\[ \frac{6x^2 + 17x - 40}{x^2 + x - 20} + \frac{3}{x - 4} - \frac{5x}{x + 5} \]
Let's break down and simplify this expression step by step.
1. **Identify Common Factors:**
- Factorize the quadratic expressions in the denominators, if possible.
- Determine a common denominator that can simplify the addition and subtraction of these rational expressions.
2. **Simplify Each Term:**
- Simplify the individual fractions before attempting to combine them.
3. **Combine the Fractions:**
- Once simplified, use the common denominator to combine the terms into a single rational expression.
4. **Check for Any Further Simplifications:**
- After combining, verify if the resulting expression can be further simplified by canceling common factors in the numerator and denominator.
By following these steps, you can effectively simplify complex algebraic expressions. Let’s apply this to the given expression and work through the solution.
---
This transcription outlines the algebraic expression and sets the stage for a step-by-step simplification process, which would be useful for educational purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa38d3af-d2a1-4c36-a58b-a982b5534c39%2Fca51a1c7-ba5c-4d04-97f4-02c44e9e867e%2Fvtbtc4a.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription of the image written for an educational website:
---
### Algebraic Expression Simplification
Consider the following algebraic expression that needs to be simplified:
\[ \frac{6x^2 + 17x - 40}{x^2 + x - 20} + \frac{3}{x - 4} - \frac{5x}{x + 5} \]
Let's break down and simplify this expression step by step.
1. **Identify Common Factors:**
- Factorize the quadratic expressions in the denominators, if possible.
- Determine a common denominator that can simplify the addition and subtraction of these rational expressions.
2. **Simplify Each Term:**
- Simplify the individual fractions before attempting to combine them.
3. **Combine the Fractions:**
- Once simplified, use the common denominator to combine the terms into a single rational expression.
4. **Check for Any Further Simplifications:**
- After combining, verify if the resulting expression can be further simplified by canceling common factors in the numerator and denominator.
By following these steps, you can effectively simplify complex algebraic expressions. Let’s apply this to the given expression and work through the solution.
---
This transcription outlines the algebraic expression and sets the stage for a step-by-step simplification process, which would be useful for educational purposes.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education